Question

收敛时要说明条件收敛或绝对收敛?

Answer 1

对通项取绝对值b(n)=|a(n)|=(n+1)!/n^(n+1)

则有b(n+1)/b(n) = (n+2)/(n+1) * [n/(n+1)]^(n+1)

对上式取n→∞,由于(n+2)/(n+1)→1

[n/(n+1)]^(n+1) = [1-1/(n+1)]^(n+1)→1/e

即有b(n+1)/b(n)→1/e