>837
 (e-1)Σ[n=1,N] n*(1/e)^n = Σ[n=1,N] (1/e)^(n-1) -N*(1/e)^N = {e-(1/e)^N }/(e-1) - N*(1/e)^N.
 Σ[n=1,N] n*(1/e)^n = {e-(1/e)^N }/(e-1)^2 - N*(1/e)^N /(e-1) → e/(e-1)^2 = 0.920673594207792… (N→∞)

>839,841
 極限は1/2でつ...