(n+3/n+1)^n当n趋近于无穷时的极限值 - 知识问答

(n+3/n+1)^n当n趋近于无穷时的极限值

2个回答

lim(n→∞)[(n+3)/(n+1)]^n
=lim(n→∞){[1+2/(n+1)]^(n+1)}/[1+2/(n+1)]
=lim(n→∞){[1+2/(n+1)]^(n+1)/2}^2/lim(n→∞)[1+2/(n+1)]
={lim[(n+1)/2→∞][1+2/(n+1)]^(n+1)/2}^2/(1+0)
=e^2/1
=e^2.

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