lim-n-e-a-n-n-Here-a-R-

Question Number 34951 by rahul 19 last updated on 13/May/18

\lim_{n \to \infty} {(\frac{e \times a}{n})}^{n} = ?

H e r e a ϵ R^{+}

Answered by MJS last updated on 14/May/18

a e = p \in R^{+}

\lim_{n \to \infty} \frac{p^{n}}{n^{n}} = L

L = \lim_{n \to \infty} \frac{p^{n}}{n^{n}} = \lim_{n \to \infty} \frac{\frac{d}{d n} [p^{n}]}{\frac{d}{d n} [n^{n}]} = \lim_{n \to \infty} \frac{\ln (p) \times p^{n}}{(1 + \ln (n)) \times n^{n}} =

= L \times \lim_{n \to \infty} \frac{\ln (p)}{1 + \ln (n)} = L \times 0 = 0

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