分享一下通过LaTeX盖楼

mathematica

$\frac{1}\frac{2}\frac{3}\frac{4}\frac{5}\frac{6}\frac{7}\frac{8}\frac{9}\frac{10}\frac{11}\frac{12}\frac{13}\frac{14}\frac{15}\frac{16}\frac{17}\frac{18}\frac{19}\frac{20}\frac{21}\frac{22}\frac{23}\frac{24}\frac{25}\frac{26}\frac{27}\frac{28}\frac{29}\frac{30}\frac{31}\frac{32}\frac{33}\frac{34}\frac{35}\frac{36}\frac{37}\frac{38}\frac{39}\frac{40}\frac{41}\frac{42}\frac{43}\frac{44}\frac{45}\frac{46}\frac{47}\frac{48}\frac{49}\frac{50}\frac{51}\frac{52}\frac{53}\frac{54}\frac{55}\frac{56}\frac{57}\frac{58}\frac{59}\frac{60}\frac{61}\frac{62}\frac{63}\frac{64}\frac{65}\frac{66}\frac{67}\frac{68}\frac{69}\frac{70}\frac{71}\frac{72}\frac{73}\frac{74}\frac{75}\frac{76}\frac{77}\frac{78}\frac{79}{80}$

1. \frac{1}\frac{2}\frac{3}\frac{4}\frac{5}\frac{6}\frac{7}\frac{8}\frac{9}\frac{10}\frac{11}\frac{12}\frac{13}\frac{14}\frac{15}\frac{16}\frac{17}\frac{18}\frac{19}\frac{20}\frac{21}\frac{22}\frac{23}\frac{24}\frac{25}\frac{26}\frac{27}\frac{28}\frac{29}\frac{30}\frac{31}\frac{32}\frac{33}\frac{34}\frac{35}\frac{36}\frac{37}\frac{38}\frac{39}\frac{40}\frac{41}\frac{42}\frac{43}\frac{44}\frac{45}\frac{46}\frac{47}\frac{48}\frac{49}\frac{50}\frac{51}\frac{52}\frac{53}\frac{54}\frac{55}\frac{56}\frac{57}\frac{58}\frac{59}\frac{60}\frac{61}\frac{62}\frac{63}\frac{64}\frac{65}\frac{66}\frac{67}\frac{68}\frac{69}\frac{70}\frac{71}\frac{72}\frac{73}\frac{74}\frac{75}\frac{76}\frac{77}\frac{78}\frac{79}\frac{80}\frac{81}\frac{82}\frac{83}\frac{84}\frac{85}\frac{86}\frac{87}\frac{88}\frac{89}\frac{90}\frac{91}\frac{92}\frac{93}\frac{94}\frac{95}\frac{96}\frac{97}\frac{98}\frac{99}\frac{100}\frac{101}\frac{102}\frac{103}\frac{104}\frac{105}\frac{106}\frac{107}\frac{108}\frac{109}\frac{110}\frac{111}\frac{112}\frac{113}\frac{114}\frac{115}\frac{116}\frac{117}\frac{118}\frac{119}\frac{120}\frac{121}\frac{122}\frac{123}\frac{124}\frac{125}\frac{126}\frac{127}\frac{128}\frac{129}\frac{130}\frac{131}\frac{132}\frac{133}\frac{134}\frac{135}\frac{136}\frac{137}\frac{138}\frac{139}\frac{140}\frac{141}\frac{142}\frac{143}\frac{144}\frac{145}\frac{146}\frac{147}\frac{148}\frac{149}{150}

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1. #通过循环,由内向外,不断增加底
   
2. use strict;use warnings;use diagnostics;
   
3. #指数形式的楼
   
4. my $str='8^{8}';
   
5. my $i=0;
   
6. while($i<50)
   
7. {
   
8.     $str='8^{' . $str . '}';
   
9.     $i++;
   
10. }
    
11. #输出结果
    
12. open(FH,">out2.txt");
    
13. print FH $str;
    
14. print FH "\n";
    
15. close(FH);
    
16. 
    
17. #分数形式的楼
    
18. $str="\\frac{1}";
    
19. $i=2;
    
20. while($i<150)
    
21. {
    
22.     $str=$str . "\\frac{" . "$i" . "}";
    
23.     $i++;
    
24. }
    
25. $str=$str . "{" . "$i" . "}";
    
26. #输出结果
    
27. open(FH,">>out2.txt");
    
28. print FH $str;
    
29. close(FH);
    

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KeyTo9_Fans

$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac{7}{8}}}}{\frac{\frac{\frac{9}{10}}{\frac{11}{12}}}{\frac{\frac{13}{14}}{\frac{15}{16}}}}}{\frac{\frac{\frac{\frac{17}{18}}{\frac{19}{20}}}{\frac{\frac{21}{22}}{\frac{23}{24}}}}{\frac{\frac{\frac{25}{26}}{\frac{27}{28}}}{\frac{\frac{29}{30}}{\frac{31}{32}}}}}}{\frac{\frac{\frac{\frac{\frac{33}{34}}{\frac{35}{36}}}{\frac{\frac{37}{38}}{\frac{39}{40}}}}{\frac{\frac{\frac{41}{42}}{\frac{43}{44}}}{\frac{\frac{45}{46}}{\frac{47}{48}}}}}{\frac{\frac{\frac{\frac{49}{50}}{\frac{51}{52}}}{\frac{\frac{53}{54}}{\frac{55}{56}}}}{\frac{\frac{\frac{57}{58}}{\frac{59}{60}}}{\frac{\frac{61}{62}}{\frac{63}{64}}}}}}}{\frac{\frac{\frac{\frac{\frac{\frac{65}{66}}{\frac{67}{68}}}{\frac{\frac{69}{70}}{\frac{71}{72}}}}{\frac{\frac{\frac{73}{74}}{\frac{75}{76}}}{\frac{\frac{77}{78}}{\frac{79}{80}}}}}{\frac{\frac{\frac{\frac{81}{82}}{\frac{83}{84}}}{\frac{\frac{85}{86}}{\frac{87}{88}}}}{\frac{\frac{\frac{89}{90}}{\frac{91}{92}}}{\frac{\frac{93}{94}}{\frac{95}{96}}}}}}{\frac{\frac{\frac{\frac{\frac{97}{98}}{\frac{99}{100}}}{\frac{\frac{101}{102}}{\frac{103}{104}}}}{\frac{\frac{\frac{105}{106}}{\frac{107}{108}}}{\frac{\frac{109}{110}}{\frac{111}{112}}}}}{\frac{\frac{\frac{\frac{113}{114}}{\frac{115}{116}}}{\frac{\frac{117}{118}}{\frac{119}{120}}}}{\frac{\frac{\frac{121}{122}}{\frac{123}{124}}}{\frac{\frac{125}{126}}{\frac{127}{128}}}}}}}}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{129}{130}}{\frac{131}{132}}}{\frac{\frac{133}{134}}{\frac{135}{136}}}}{\frac{\frac{\frac{137}{138}}{\frac{139}{140}}}{\frac{\frac{141}{142}}{\frac{143}{144}}}}}{\frac{\frac{\frac{\frac{145}{146}}{\frac{147}{148}}}{\frac{\frac{149}{150}}{\frac{151}{152}}}}{\frac{\frac{\frac{153}{154}}{\frac{155}{156}}}{\frac{\frac{157}{158}}{\frac{159}{160}}}}}}{\frac{\frac{\frac{\frac{\frac{161}{162}}{\frac{163}{164}}}{\frac{\frac{165}{166}}{\frac{167}{168}}}}{\frac{\frac{\frac{169}{170}}{\frac{171}{172}}}{\frac{\frac{173}{174}}{\frac{175}{176}}}}}{\frac{\frac{\frac{\frac{177}{178}}{\frac{179}{180}}}{\frac{\frac{181}{182}}{\frac{183}{184}}}}{\frac{\frac{\frac{185}{186}}{\frac{187}{188}}}{\frac{\frac{189}{190}}{\frac{191}{192}}}}}}}{\frac{\frac{\frac{\frac{\frac{\frac{193}{194}}{\frac{195}{196}}}{\frac{\frac{197}{198}}{\frac{199}{200}}}}{\frac{\frac{\frac{201}{202}}{\frac{203}{204}}}{\frac{\frac{205}{206}}{\frac{207}{208}}}}}{\frac{\frac{\frac{\frac{209}{210}}{\frac{211}{212}}}{\frac{\frac{213}{214}}{\frac{215}{216}}}}{\frac{\frac{\frac{217}{218}}{\frac{219}{220}}}{\frac{\frac{221}{222}}{\frac{223}{224}}}}}}{\frac{\frac{\frac{\frac{\frac{225}{226}}{\frac{227}{228}}}{\frac{\frac{229}{230}}{\frac{231}{232}}}}{\frac{\frac{\frac{233}{234}}{\frac{235}{236}}}{\frac{\frac{237}{238}}{\frac{239}{240}}}}}{\frac{\frac{\frac{\frac{241}{242}}{\frac{243}{244}}}{\frac{\frac{245}{246}}{\frac{247}{248}}}}{\frac{\frac{\frac{249}{250}}{\frac{251}{252}}}{\frac{\frac{253}{254}}{\frac{255}{256}}}}}}}}}{...}=\sqrt{2}/2$

\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac{7}{8}}}}{\frac{\frac{\frac{9}{10}}{\frac{11}{12}}}{\frac{\frac{13}{14}}{\frac{15}{16}}}}}{\frac{\frac{\frac{\frac{17}{18}}{\frac{19}{20}}}{\frac{\frac{21}{22}}{\frac{23}{24}}}}{\frac{\frac{\frac{25}{26}}{\frac{27}{28}}}{\frac{\frac{29}{30}}{\frac{31}{32}}}}}}{\frac{\frac{\frac{\frac{\frac{33}{34}}{\frac{35}{36}}}{\frac{\frac{37}{38}}{\frac{39}{40}}}}{\frac{\frac{\frac{41}{42}}{\frac{43}{44}}}{\frac{\frac{45}{46}}{\frac{47}{48}}}}}{\frac{\frac{\frac{\frac{49}{50}}{\frac{51}{52}}}{\frac{\frac{53}{54}}{\frac{55}{56}}}}{\frac{\frac{\frac{57}{58}}{\frac{59}{60}}}{\frac{\frac{61}{62}}{\frac{63}{64}}}}}}}{\frac{\frac{\frac{\frac{\frac{\frac{65}{66}}{\frac{67}{68}}}{\frac{\frac{69}{70}}{\frac{71}{72}}}}{\frac{\frac{\frac{73}{74}}{\frac{75}{76}}}{\frac{\frac{77}{78}}{\frac{79}{80}}}}}{\frac{\frac{\frac{\frac{81}{82}}{\frac{83}{84}}}{\frac{\frac{85}{86}}{\frac{87}{88}}}}{\frac{\frac{\frac{89}{90}}{\frac{91}{92}}}{\frac{\frac{93}{94}}{\frac{95}{96}}}}}}{\frac{\frac{\frac{\frac{\frac{97}{98}}{\frac{99}{100}}}{\frac{\frac{101}{102}}{\frac{103}{104}}}}{\frac{\frac{\frac{105}{106}}{\frac{107}{108}}}{\frac{\frac{109}{110}}{\frac{111}{112}}}}}{\frac{\frac{\frac{\frac{113}{114}}{\frac{115}{116}}}{\frac{\frac{117}{118}}{\frac{119}{120}}}}{\frac{\frac{\frac{121}{122}}{\frac{123}{124}}}{\frac{\frac{125}{126}}{\frac{127}{128}}}}}}}}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{129}{130}}{\frac{131}{132}}}{\frac{\frac{133}{134}}{\frac{135}{136}}}}{\frac{\frac{\frac{137}{138}}{\frac{139}{140}}}{\frac{\frac{141}{142}}{\frac{143}{144}}}}}{\frac{\frac{\frac{\frac{145}{146}}{\frac{147}{148}}}{\frac{\frac{149}{150}}{\frac{151}{152}}}}{\frac{\frac{\frac{153}{154}}{\frac{155}{156}}}{\frac{\frac{157}{158}}{\frac{159}{160}}}}}}{\frac{\frac{\frac{\frac{\frac{161}{162}}{\frac{163}{164}}}{\frac{\frac{165}{166}}{\frac{167}{168}}}}{\frac{\frac{\frac{169}{170}}{\frac{171}{172}}}{\frac{\frac{173}{174}}{\frac{175}{176}}}}}{\frac{\frac{\frac{\frac{177}{178}}{\frac{179}{180}}}{\frac{\frac{181}{182}}{\frac{183}{184}}}}{\frac{\frac{\frac{185}{186}}{\frac{187}{188}}}{\frac{\frac{189}{190}}{\frac{191}{192}}}}}}}{\frac{\frac{\frac{\frac{\frac{\frac{193}{194}}{\frac{195}{196}}}{\frac{\frac{197}{198}}{\frac{199}{200}}}}{\frac{\frac{\frac{201}{202}}{\frac{203}{204}}}{\frac{\frac{205}{206}}{\frac{207}{208}}}}}{\frac{\frac{\frac{\frac{209}{210}}{\frac{211}{212}}}{\frac{\frac{213}{214}}{\frac{215}{216}}}}{\frac{\frac{\frac{217}{218}}{\frac{219}{220}}}{\frac{\frac{221}{222}}{\frac{223}{224}}}}}}{\frac{\frac{\frac{\frac{\frac{225}{226}}{\frac{227}{228}}}{\frac{\frac{229}{230}}{\frac{231}{232}}}}{\frac{\frac{\frac{233}{234}}{\frac{235}{236}}}{\frac{\frac{237}{238}}{\frac{239}{240}}}}}{\frac{\frac{\frac{\frac{241}{242}}{\frac{243}{244}}}{\frac{\frac{245}{246}}{\frac{247}{248}}}}{\frac{\frac{\frac{249}{250}}{\frac{251}{252}}}{\frac{\frac{253}{254}}{\frac{255}{256}}}}}}}}}{...}=\sqrt{2}/2

1. #include<cstdio>
   
2. 
   
3. int s;
   
4. FILE *f;
   
5. 
   
6. void p(int i)
   
7. {
   
8.         fprintf(f,"\\frac");
   
9.         if(!i)fprintf(f,"{%d}{%d}",s+1,s+2),s+=2;
   
10.         else fprintf(f,"{"),p(i-1),fprintf(f,"}{"),p(i-1),fprintf(f,"}");
    
11. }
    
12. 
    
13. int main()
    
14. {
    
15.         f=fopen("d:\\frac.txt","w");
    
16.         fprintf(f,"\frac{"),p(7),fprintf(f,"}{...}=\sqrt{2}/2");
    
17.         fclose(f);
    
18.         return 0;
    
19. }

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上述式子的极限值竟然恰好是$\sqrt{2}/2$，如何证明？

mathematica

KeyTo9_Fans 发表于 2018-11-16 13:58
$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac ...

$\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\sqrt{6+\sqrt{7+\sqrt{8+\sqrt{9+\sqrt{10+\sqrt{11+\sqrt{12+\sqrt{13+\sqrt{14+\sqrt{15+\sqrt{16+\sqrt{17+\sqrt{18+\sqrt{19+\sqrt{20+\sqrt{21+\sqrt{22+\sqrt{23+\sqrt{24+\sqrt{25+\sqrt{26+\sqrt{27+\sqrt{28+\sqrt{29+\sqrt{30+\sqrt{31+\sqrt{32+\sqrt{33+\sqrt{34+\sqrt{35+\sqrt{36+\sqrt{37+\sqrt{38+\sqrt{39+\sqrt{40+\sqrt{41+\sqrt{42+\sqrt{43+\sqrt{44+\sqrt{45+\sqrt{46+\sqrt{47+\sqrt{48+\sqrt{49+\sqrt{50}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

1. \sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\sqrt{6+\sqrt{7+\sqrt{8+\sqrt{9+\sqrt{10+\sqrt{11+\sqrt{12+\sqrt{13+\sqrt{14+\sqrt{15+\sqrt{16+\sqrt{17+\sqrt{18+\sqrt{19+\sqrt{20+\sqrt{21+\sqrt{22+\sqrt{23+\sqrt{24+\sqrt{25+\sqrt{26+\sqrt{27+\sqrt{28+\sqrt{29+\sqrt{30+\sqrt{31+\sqrt{32+\sqrt{33+\sqrt{34+\sqrt{35+\sqrt{36+\sqrt{37+\sqrt{38+\sqrt{39+\sqrt{40+\sqrt{41+\sqrt{42+\sqrt{43+\sqrt{44+\sqrt{45+\sqrt{46+\sqrt{47+\sqrt{48+\sqrt{49+\sqrt{50}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
   

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perl语言代码

1. #通过循环,由内向外,不断增加底
   
2. use strict;use warnings;use diagnostics;
   
3. #开平方
   
4. my $i=50;
   
5. my $str="\\sqrt{$i}";
   
6. $i--;
   
7. while($i>1)
   
8. {
   
9.     $str="\\sqrt{$i+" . $str . '}';
   
10.     $i--;
    
11. }
    
12. $str="\\sqrt{$i+" . $str . '}';
    
13. #输出结果
    
14. open(FH,">out2.txt");
    
15. print FH $str;
    
16. close(FH);
    

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mathematica

KeyTo9_Fans 发表于 2018-11-16 13:58
$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac ...

不知道你这表达式是什么意思,我区分不了分子分母

mathematica

\[\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{3}}{4}}{5}}{6}}{7}}{8}}{9}}{10}}{11}}{12}}{13}}{14}}{15}}{16}}{17}}{18}}{19}}{20}}{21}}{22}}{23}}{24}}{25}}{26}}{27}}{28}}{29}}{30}}{31}}{32}}{33}}{34}}{35}}{36}}{37}}{38}}{39}}{40}}{41}}{42}}{43}}{44}}{45}}{46}}{47}}{48}}{49}}{50}}{51}}{52}}{53}}{54}}{55}}{56}}{57}}{58}}{59}}{60}}{61}}{62}}{63}}{64}}{65}}{66}}{67}}{68}}{69}}{70}}{71}}{72}}{73}}{74}}{75}}{76}}{77}}{78}}{79}}{80}\]

1. \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{3}}{4}}{5}}{6}}{7}}{8}}{9}}{10}}{11}}{12}}{13}}{14}}{15}}{16}}{17}}{18}}{19}}{20}}{21}}{22}}{23}}{24}}{25}}{26}}{27}}{28}}{29}}{30}}{31}}{32}}{33}}{34}}{35}}{36}}{37}}{38}}{39}}{40}}{41}}{42}}{43}}{44}}{45}}{46}}{47}}{48}}{49}}{50}

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1. #通过循环,由内向外,不断增加底
   
2. use strict;use warnings;use diagnostics;
   
3. #开平方
   
4. my $str="\\frac{1}{2}";
   
5. my $i=3;
   
6. while($i<50)
   
7. {
   
8.     $str="\\frac{" . $str . "}{$i}";
   
9.     $i++
   
10. }
    
11. $str="\\frac{" . $str . "}{$i}";
    
12. #输出结果
    
13. open(FH,">out2.txt");
    
14. print FH $str;
    
15. close(FH);
    

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\[\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{3}}{4}}{5}}{6}}{7}}{8}}{9}}{10}}{11}}{12}}{13}}{14}}{15}}{16}}{17}}{18}}{19}}{20}}{21}}{22}}{23}}{24}}{25}}{26}}{27}}{28}}{29}}{30}}{31}}{32}}{33}}{34}}{35}}{36}}{37}}{38}}{39}}{40}}{41}}{42}}{43}}{44}}{45}}{46}}{47}}{48}}{49}}{50}}{51}}{52}}{53}}{54}}{55}}{56}}{57}}{58}}{59}}{60}}{61}}{62}}{63}}{64}}{65}}{66}}{67}}{68}}{69}}{70}}{71}}{72}}{73}}{74}}{75}}{76}}{77}}{78}}{79}}{80}}{81}}{82}}{83}}{84}}{85}}{86}}{87}}{88}}{89}}{90}}{91}}{92}}{93}}{94}}{95}}{96}}{97}}{98}}{99}}{100}}{101}}{102}}{103}}{104}}{105}}{106}}{107}}{108}}{109}}{110}}{111}}{112}}{113}}{114}}{115}}{116}}{117}}{118}}{119}}{120}}{121}}{122}}{123}}{124}}{125}}{126}}{127}}{128}}{129}}{130}}{131}}{132}}{133}}{134}}{135}}{136}}{137}}{138}}{139}}{140}}{141}}{142}}{143}}{144}}{145}}{146}}{147}}{148}}{149}}{150}
\]

mathematica

\[\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{3}}{4}}{5}}{6}}{7}}{8}}{9}}{10}}{11}}{12}}{13}}{14}}{15}}{16}}{17}}{18}}{19}}{20}}{21}}{22}}{23}}{24}}{25}}{26}}{27}}{28}}{29}}{30}}{31}}{32}}{33}}{34}}{35}}{36}}{37}}{38}}{39}}{40}}{41}}{42}}{43}}{44}}{45}}{46}}{47}}{48}}{49}}{50}}{51}}{52}}{53}}{54}}{55}}{56}}{57}}{58}}{59}}{60}}{61}}{62}}{63}}{64}}{65}}{66}}{67}}{68}}{69}}{70}}{71}}{72}}{73}}{74}}{75}}{76}}{77}}{78}}{79}}{80}}{81}}{82}}{83}}{84}}{85}}{86}}{87}}{88}}{89}}{90}}{91}}{92}}{93}}{94}}{95}}{96}}{97}}{98}}{99}}{100}}{101}}{102}}{103}}{104}}{105}}{106}}{107}}{108}}{109}}{110}}{111}}{112}}{113}}{114}}{115}}{116}}{117}}{118}}{119}}{120}}{121}}{122}}{123}}{124}}{125}}{126}}{127}}{128}}{129}}{130}}{131}}{132}}{133}}{134}}{135}}{136}}{137}}{138}}{139}}{140}}{141}}{142}}{143}}{144}}{145}}{146}}{147}}{148}}{149}}{150}}{151}}{152}}{153}}{154}}{155}}{156}}{157}}{158}}{159}}{160}}{161}}{162}}{163}}{164}}{165}}{166}}{167}}{168}}{169}}{170}}{171}}{172}}{173}}{174}}{175}}{176}}{177}}{178}}{179}}{180}}{181}}{182}}{183}}{184}}{185}}{186}}{187}}{188}}{189}}{190}}{191}}{192}}{193}}{194}}{195}}{196}}{197}}{198}}{199}}{200}}{201}}{202}}{203}}{204}}{205}}{206}}{207}}{208}}{209}}{210}}{211}}{212}}{213}}{214}}{215}}{216}}{217}}{218}}{219}}{220}}{221}}{222}}{223}}{224}}{225}}{226}}{227}}{228}}{229}}{230}}{231}}{232}}{233}}{234}}{235}}{236}}{237}}{238}}{239}}{240}}{241}}{242}}{243}}{244}}{245}}{246}}{247}}{248}}{249}}{250}\]

mathematica

\[120^{119^{118^{117^{116^{115^{114^{113^{112^{111^{110^{109^{108^{107^{106^{105^{104^{103^{102^{101^{100^{99^{98^{97^{96^{95^{94^{93^{92^{91^{90^{89^{88^{87^{86^{85^{84^{83^{82^{81^{80^{79^{78^{77^{76^{75^{74^{73^{72^{71^{70^{69^{68^{67^{66^{65^{64^{63^{62^{61^{60^{59^{58^{57^{56^{55^{54^{53^{52^{51^{50^{49^{48^{47^{46^{45^{44^{43^{42^{41^{40^{39^{38^{37^{36^{35^{34^{33^{32^{31^{30^{29^{28^{27^{26^{25^{24^{23^{22^{21^{20^{19^{18^{17^{16^{15^{14^{13^{12^{11^{10^{9^{8^{7^{6^{5^{4^{3^{2^{1}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\]

mathematica

\[200^{199^{198^{197^{196^{195^{194^{193^{192^{191^{190^{189^{188^{187^{186^{185^{184^{183^{182^{181^{180^{179^{178^{177^{176^{175^{174^{173^{172^{171^{170^{169^{168^{167^{166^{165^{164^{163^{162^{161^{160^{159^{158^{157^{156^{155^{154^{153^{152^{151^{150^{149^{148^{147^{146^{145^{144^{143^{142^{141^{140^{139^{138^{137^{136^{135^{134^{133^{132^{131^{130^{129^{128^{127^{126^{125^{124^{123^{122^{121^{120^{119^{118^{117^{116^{115^{114^{113^{112^{111^{110^{109^{108^{107^{106^{105^{104^{103^{102^{101^{100^{99^{98^{97^{96^{95^{94^{93^{92^{91^{90^{89^{88^{87^{86^{85^{84^{83^{82^{81^{80^{79^{78^{77^{76^{75^{74^{73^{72^{71^{70^{69^{68^{67^{66^{65^{64^{63^{62^{61^{60^{59^{58^{57^{56^{55^{54^{53^{52^{51^{50^{49^{48^{47^{46^{45^{44^{43^{42^{41^{40^{39^{38^{37^{36^{35^{34^{33^{32^{31^{30^{29^{28^{27^{26^{25^{24^{23^{22^{21^{20^{19^{18^{17^{16^{15^{14^{13^{12^{11^{10^{9^{8^{7^{6^{5^{4^{3^{2^{1}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\]

mathematica

\[\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac{7}{8}}}\]


perl代码

1. use strict;use warnings;use diagnostics;
   
2. my $str="\\frac{1}{2}";
   
3. my $add=2;
   
4. my $fm;
   
5. my $i=1;
   
6. while($i<3)#最大的数是2^7=128
   
7. {
   
8.     $fm=$str;#把分子字符串赋值给分母
   
9.     $fm=~s/(\d+)/$1+$add/eg;#分母上的各个数增加$add,e表示计算
   
10.     $str="\\frac{$str}{$fm}";#由分子分母得到一个新的分数
    
11.     $add=$add*2;#下次增加的数乘以2，依次是2 4 8 16 32 64
    
12.     $i++;
    
13. }
    
14. #输出结果
    
15. open(FH,">out2.txt");
    
16. print FH "\\[$str\\]";
    
17. print FH "\n";
    
18. close(FH);
    

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mathematica

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