>>39

2項定理より
　{(k^2)/(k^2 -1)}^(k+1) = {1 +1/(k^2 -1)}^(k+1) = Σ[j=0,k+1] Ｃ[k+1,j] /(k^2 -1)^j > 1 + 1/(k-1) = k/(k-1),

∴　{k/(k-1)}^k > {(k+1)/k}^(k+1) > ･･･(単調減少)･･･ > lim[k→∞) (1 + 1/k)^k = e,