- 769 名前：１３２人目の素数さん mailto:sage [2008/01/01(火) 19:48:50 ]
- >>742
log(1+x) = log(x) +(1/x) -O(1/2x^2) より
(log(1+x))^(m+1) - (log(x))^(m+1) = (m+1)*{1 -O(1/2x)}(1/x)(log(x))^m,
{(log(1+x))^(m+1) - (log(x))^(m+1)}^n = (m+1)^n*{1 -O(n/2x)}(1/x^n)(log(x))^(mn),
x^(n-m)*{(log(1+x))^(m+1) - (log(x))^(m+1)}^n / {(log(1+x))^(n+1) - (log(x))^(n+1)}^m
= {(m+1)^n/(n+1)^m}｛1 +O((m-n)/2x)}
→ (m+1)^n/(n+1)^m (x→∞)
m=98, n=100,
>743
(x^2)*{ [(log(1+x))^99 - (log(x))^99]／log(x)^98 }^2 〜 99^2 の間違い。
