比值审敛法∑(1→∞)(2∧n×n!)/n∧n收敛

问题描述:

比值审敛法∑(1→∞)(2∧n×n!)/n∧n收敛

ρ = lim a/a
= lim 2^(n+1)*(n+1)!*n^n/[2^n*n!*(n+1)^(n+1)]
= lim 2n^n/[(n+1)^n]
= lim 2/[(1+1/n)^n] = 2/e 故原级数收敛.