爱开玩笑的极限
1,这串数没有长大,可就是找不到极限。
\(\frac{1}{10^{0}}+\frac{3}{10^{1}}+\frac{6}{10^{3}}+\frac{10}{10^{6}}+\frac{15}{10^{10}}+\frac{21}{10^{15}}+...+\frac{k(k+1)/2}{10^{k(k-1)/2}}\)
1.3060100015000210000280000036000000450000000550000000066...
2,这串数长得很大,可极限就不是\(\infty\) 。
\(1^1+2^2+3^3+4^4+5^5+6^6+7^7+8^8+...+k^k\)
1, 5, 32, 288, 3413, 50069, 873612, 17650828, 405071317,
10405071317, 295716741928, 9211817190184, 312086923782437,
11424093749340453, 449317984130199828, ..........
$s(n) = 1^1+ 2^2+ 3^3+ 4^4+...+n^n$
$n^n*(1 +frac{1}{4(n−1)})< s(n) < n^n(1 +frac{2}{e(n−1)})$
参考文献:http://ijpam.eu/contents/2007-36-2/9/9.pdf 本帖最后由 王守恩 于 2020-3-26 10:44 编辑
northwolves 发表于 2020-3-25 21:01
$s(n) = 1^1+ 2^2+ 3^3+ 4^4+...+n^n$
$n^n*(1 +frac{1}{4(n−1)})< s(n) < n^n(1 +frac{2}{e(nͨ ...
开心茶馆开心就好。这样也可以的?
$s(n) = 1^1+ 2^2+ 3^3+ 4^4+...+n^n$
$n^n*(1 +frac{2}{e^2(n−1)})< s(n) < n^n*(1 +frac{1}{e(n-1)))$ 开心茶馆开心就好。
\(\D\frac{1}{10^{0}}+\frac{3}{10^{1}}+\frac{6}{10^{3}}+\frac{10}{10^{6}}+\frac{15}{10^{10}}+\frac{21}{10^{15}}+\frac{28}{10^{21}}+\frac{36}{10^{28}}+\frac{45}{10^{36}}+\cdots\cdots+\frac{n(n+1)/2}{10^{n(n-1)/2}}\)
N, 100]
1.306010001500021000028000003600000045000000055000000000000000000000000000000000000000000000000000000
N, 100]
1.306010001500021000028000003600000045000000055000000006600000000078000000000091000000000010500000000
N, 100]
1.306010001500021000028000003600000045000000055000000006600000000078000000000091000000000010500000000
N, 100]
1.306010001500021000028000003600000045000000055000000006600000000078000000000091000000000010500000000
N, 100]
1.306010001500021000028000003600000045000000055000000006600000000078000000000091000000000010500000000
Sum
1.3060100015000210000280000036000000450000000550000000066000000000780000000000910000000000105000000000001200000000000001360000000000000153000000
00000000171000000000000000190000000000000000021000000000000000000231000000000000000000253000000000000000000027600000000000000000000300000000000000000000000
325000000000000000000000035100000000000000000000000378000000000000000000000000406000000000000000000000000043500000000000000000000000000465000000000000000000000000000496
000000000000000000000000000052800000000000000000000000000000561000000000000000000000000000000595000000000000000000000000000000063000000000000000000000000000000000666000000000000000000......
\(\D\sum_{n=1}^{\infty}\frac{n(n+1)}{\sqrt{4\times10^{n(n-1)/2}}}\)
这串数没有长大,可就是找不到极限。 无穷大
1, 作线段AB, 长度为1。
始点(左)为A, 终点(右)为B。
2, 我们记C为线段AB上的任意一点。
3, C=0.500, 则AC : CB=0.500 : 0.500,
C=0.600, 则AC : CB=0.600 : 0.400,
C=0.700, 则AC : CB=0.700 : 0.300,
C=0.800, 则AC : CB=0.800 : 0.200,
C=0.900, 则AC : CB=0.900 : 0.100,
C=0.990, 则AC : CB=0.990 : 0.010,
C=0.999, 则AC : CB=0.999 : 0.001,
C=0.9999, 则AC : CB=0.9999 : 0.0001,
C=0.99999, 则AC : CB=0.99999 : 0.00001,
C=0.999999, 则AC : CB=0.999999 : 0.000001,.
C=0.999999..., 则AC : CB=0.999999... : 0.000000...,
......
4, 0.999999...... : 0.000000......, 这就是无穷大。
5, 什么叫无穷大, 这就是无穷大!!!
6, 不要认为无穷大是一个大得无法想象的数。
7, 在长度为1的线段上就可以描述出无穷大。
8, 至于从什么时候开始, AC : CB变成无穷大了, 谁也说不清楚。
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