Find the limit, when n ® of (\frac{(n!)^{1/n}}{n}) | MATH - FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION | SolveeIt | Solveeit

Today, August 18

Question

Find the limit, when n ® of $\frac{(n!)^{1/n}}{n}$

A

e

B

$\frac{1}{e^{2}}$

C

$\frac{1}{e}$

D

e²

Answer

$\frac{1}{e}$

Explanation

Solution

Let P = $\frac { ( \mathrm { n } ! ) ^ { 1 / n } } { n }$

= =

=

=

Taking logarithm then

ln P =

=

= (1n x . x – x) $\left. \right| _ { 0 } ^ { 1 }$

= – 1 – 0

= –1

Hence P = e^–1 = 1/e.