∞ 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 ----------------------------------------------------------------------------------
∞ 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