∞ Σ 3n^n/(1+n)^n 判定收敛性 n=1∞ -------------------------------------------------------------------------------------------------------------Σ 3n^n/(1+n)^n ----------------------------------------------------------------------------------
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![∞ Σ 3n^n/(1+n)^n 判定收敛性 n=1∞ -------------------------------------------------------------------------------------------------------------Σ 3n^n/(1+n)^n ----------------------------------------------------------------------------------](/uploads/image/z/8921477-29-7.jpg?t=%E2%88%9E+%CE%A3+3n%5En%2F%281%2Bn%29%5En+%E5%88%A4%E5%AE%9A%E6%94%B6%E6%95%9B%E6%80%A7+n%3D1%E2%88%9E+-------------------------------------------------------------------------------------------------------------%CE%A3+3n%5En%2F%281%2Bn%29%5En+----------------------------------------------------------------------------------)
∞ Σ 3n^n/(1+n)^n 判定收敛性 n=1∞ -------------------------------------------------------------------------------------------------------------Σ 3n^n/(1+n)^n ----------------------------------------------------------------------------------
∞ Σ 3n^n/(1+n)^n 判定收敛性 n=1
∞ -------------------------------------------------------------------------------------------------------------
Σ 3n^n/(1+n)^n --------------------------------------------------------------------------------------------
n=1
∞ Σ 3n^n/(1+n)^n 判定收敛性 n=1∞ -------------------------------------------------------------------------------------------------------------Σ 3n^n/(1+n)^n ----------------------------------------------------------------------------------
liman=lim3(n/1+n)^n
=3lim(1-1/(1+n))^n 【lim(1-1/(1+n))^(1+n)=e^-1=1/e】
=3/e
即通项不趋向于0,所以不收敛