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
答
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