证明当k为正整数时lim(n→∞)(1+k/n)^n=e^k
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证明当k为正整数时lim(n→∞)(1+k/n)^n=e^k
![证明当k为正整数时lim(n→∞)(1+k/n)^n=e^k](/uploads/image/z/1148236-52-6.jpg?t=%E8%AF%81%E6%98%8E%E5%BD%93k%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%E6%97%B6lim%28n%E2%86%92%E2%88%9E%29%281%2Bk%2Fn%29%5En%3De%5Ek)
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
=lim(n→∞)(1+k/n)^(n/k * k)
=[lim(n→∞)(1+k/n)^n/k]^k
=(e)^k
=e^k
证明当k为正整数时lim(n→∞)(1+k/n)^n=e^k
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