99/98的小数很有意思

cn8888

仔细观看吧.

1. N[99/98, 100]

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结果

1. 1.010204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653

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cn8888

N[999/998, 100]
1.001002004008016032064128256513026052104208416833667334669338677354709418837675350701402805611222445

cn8888

In[23]:= N[1/99998, 100]

Out[23]= 0.\
0000100002000040000800016000320006400128002560051201024020480409608192\
1638432768655373107462149242984860
偶然发现的,发上来供大家欣赏...........

倪举鹏

1.01020408163265306122448979591836734693877551020408163265306122448979591836734693877551020408163265其实这里就包含了这个数列所有，后面的只是穿插形式的显示出来653061225=6400000+1280000+2560+

sunwukong

\(\D\frac{10^n-1}{10^n-2}=1+\frac{\frac{1}{10^n}}{1-\frac{2}{10^n}}=1+\frac{1}{10^n}+\frac{1}{10^n}*\frac{2}{10^n}+\frac{1}{10^n}*(\frac{2}{10^n})^2+\frac{1}{10^n}*(\frac{2}{10^n})^3+...\)

sunwukong

类似的；

1. N[1/9997, 100]

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结果

0.00001000030000900027000810024300729021870656119683590507715231456943708311249337480124403732111963358901

.·.·.

记得初中时候做过类似的竞赛题
Sum[Fib(n)/10^n,{n,1,Infinity}],其中Fib(n)是第n个斐波那契数
当初强行手算了好久，大约算到了
0.112359550561797752
嗯，答案是10/89

其实就是高中等差乘等比数列求和的扩展
解法无外乎错位相减

王守恩

.·.·. 发表于 2017-12-7 19:01
记得初中时候做过类似的竞赛题
Sum[Fib(n)/10^n,{n,1,Infinity}],其中Fib(n)是第n个斐波那契数
当初强行 ...

求助：既约分数  a / b，a =？，b =？，循环节有 39996 位。答案可以有吗？
循环节=0001000200030004000500060007000800090010......9996999799989999 。

王守恩

王守恩 发表于 2018-5-23 05:59
求助：既约分数  a / b，a =？，b =？，循环节有 39996 位。答案可以有吗？
循环节=00010002000300040 ...

求助：既约分数  a / b，a =？，b =？，循环节有 39996 位。答案可以有吗？

\(既约分数\frac{a}{b}的循环节=0001,0002,0003,0004,0005,0006,0007,0008,0009,0010,......9996,9997,9998,9999,0001,0002,0003,...\)

\(\frac{10000}{99980001}的循环节=0001,0002,0003,0004,0005,0006,0007,0008,0009,0010,......9996,9997,9999,0000，0001,0002,0003,...\)

谢谢KeyTo9_Fans！答案好像不太一样，我再慢慢消化。

王守恩

王守恩 发表于 2018-5-25 06:33
求助：既约分数  a / b，a =？，b =？，循环节有 39996 位。答案可以有吗？

\(既约分数\frac{a}{b} ...

求助：既约分数  a4 / b4，a4 =？，b4 =？，循环节有 39996 位。答案可以有吗？

\(\frac{a_{1}}{b_{1}}=\frac{13717421}{111111111}\)
\(\frac{a_{1}}{b_{1}}的循环节=1,2,3,4,5,6,7,8,9,1,2,3,...\)
\(\frac{10}{81}的循环节=1,2,3,4,5,6,7,9,0,1,2,3,...\)

   \(\frac{a_{2}}{b_{2}}=\frac{10306101521283645...计195位}{1010101010101010101...计197位}\)
   \(\frac{a_{2}}{b_{2}}的循环节=01,02,03,04,05,06,07,08,09,10,......96,97,98,99,01,02,03,...\)
\(\frac{100}{9801}的循环节=01,02,03,04,05,06,07,08,09,10,......96,97,99,00,01,02,03,...\)

       \(\frac{a_{3}}{b_{3}}=\frac{1003006010015021028036045...计2992位}{1001001001001001001001001001...计2995位}\)
       \(\frac{a_{3}}{b_{3}}的循环节=001,002,003,004,005,006,007,008,009,010,......996,997,998,999,001,002,003,...\)
\(\frac{1000}{998001}的循环节=001,002,003,004,005,006,007,008,009,010,......996,997,999,000,001,002,003,...\)

           \(\frac{a_{4}}{b_{4}}=\frac{100030006001000150021002800360045...计39989位}{1000100010001000100010001000100010001...计39993位}\)
           \(\frac{a_{4}}{b_{4}}的循环节=0001,0002,0003,0004,0005,0006,0007,0008,0009,0010,......9996,9997,9998,9999,0001,0002,0003,...\)
\(\frac{10000}{99980001}的循环节=0001,0002,0003,0004,0005,0006,0007,0008,0009,0010,......9996,9997,9999,0000，0001,0002,0003,...\)