问题标题:
【lim[(n+3)/(n+1))]^(n-2)【n无穷大】】
更新时间:2024-04-28 10:44:43
问题描述:
lim[(n+3)/(n+1))]^(n-2)【n无穷大】
蔡光东回答:
lim[(n+3)/(n+1)]^(n-2)
=lim[1+2/(n+1)]^(n-2)
=lim{[1+2/(n+1)]^[(n+1)/2]}^[(n-2)×2/(n+1)]
=lime^[2(n-2)/(n+1)]
=e^lim2(n-2)/(n+1)
=e^lim[2(1-2/n)/(1+1/n)]
=e²