n→∞求(1+a^n)1/n(a≥0)的极限

题目

n→∞求(1+a^n)1/n(a≥0)的极限

答案

lim[n→+∝] (1+a^n)^(1/n)
=e^lim[n→+∝] [ln(1+a^n)]/n
=洛必达法则=e^lim[n→+∝] (lna*a^n)/(1+a^n)
=e^lim[n→+∝] (lna)/(1+1/a^n)
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