证明当k为正整数时lim(n→∞)(1+k/n)^n=e^k

问题描述:

证明当k为正整数时lim(n→∞)(1+k/n)^n=e^k

lim(n→∞)(1+k/n)^n
=lim(n→∞)(1+k/n)^(n/k * k)
=[lim(n→∞)(1+k/n)^n/k]^k
=(e)^k
=e^k