- 842 名前：１３２人目の素数さん mailto:sage [2011/12/23(金) 13:34:13.89 ]
- >>824
lim[n→∞] { (n+1)^(n+1) / n^n - n^n / (n-1)^(n-1) }
= lim[n→∞] (1 + 1/(n-1))^(n-1) * { (2 + 2/n)*(1 - 1/(n^2))^(n-1) - 1/n Σ[k=1 to n] (1 - 1/(n^2))^(k-1) }
= e(2*1-1)
= e
(1 - 1/(n^2))^(n-1) = 1/{ (1 + 1/(n^2-1))^(n^2-1) }^(1/(n+1)) → 1/e^0 =1
1/n Σ[k=1 to n] (1 - 1/(n^2))^(k-1) → 1 になるのは、はさみうちナリよキテレツ！
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/ ／ lim ＼ ﾊﾟｶｯ！
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