If $k \ne 0$ is a constant and $n \in N$, then, $\mathop {\lim }\limits_{n \to \infty } \,\,\left\{ {\frac{{n!}}{{{{\left( {k\;n} \right)}^n}}}} \right\}$ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

k \ne 0

is a constant and

n \in N

, then,

\lim\limits_{n \to \infty } \,\,\left\{ {\frac{{n!}}{{{{\left( {k\;n} \right)}^n}}}} \right\}

is equal to

View answer and explanation

Correct option: D

\frac{1}{{ke}}

Option D (

\frac{1}{{ke}}

) is correct because the limit is evaluated using Stirling's approximation and properties of logarithms and integrals.

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