lim(1+3^n)^1/n的值。n趋近于无穷。。。求过程
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lim[n→∞] (1+3^n)^(1/n)
=e^lim[n→∞] [ln(1+3^n)]/n
=e^lim[n→∞] 3^n*ln(3)/(1+3^n),洛必达法则
=e^ln(3)lim[n→∞] 3^n/(1+3^n)
=3lim[n→∞] 3^n/(1+3^n)
=3lim[n→∞] 3^n*ln(3)/[3^n*ln(3)]
=3lim[n→∞] 1
=3
=e^lim[n→∞] [ln(1+3^n)]/n
=e^lim[n→∞] 3^n*ln(3)/(1+3^n),洛必达法则
=e^ln(3)lim[n→∞] 3^n/(1+3^n)
=3lim[n→∞] 3^n/(1+3^n)
=3lim[n→∞] 3^n*ln(3)/[3^n*ln(3)]
=3lim[n→∞] 1
=3
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