$\mathop {\lim }\limits_{n \to \infty } \,\,\frac{{{1^{99}} + \,\,{2^{99}}\,\, + \,\, \ldots + \,\,{n^{99}}}}{{{n^{100}}}} = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\lim\limits_{n \to \infty } \,\,\frac{{{1^{99}} + \,\,{2^{99}}\,\, + \,\, \ldots + \,\,{n^{99}}}}{{{n^{100}}}} =

View answer and explanation

Correct option: B

\frac{{1}}{{100}}

Option B (

\frac{{1}}{{100}}

) is correct because the limit of the sum can be expressed as a definite integral, which evaluates to

\frac{1}{100}

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