$\mathop {\lim }\limits_{n \to \infty } \,\,\frac{{1\,\, + \,\,{2^4} + \,\,{3^4} + \,\,... + \,\,{n^4}}}{{{n^5}}}\,\, - \,\,\mathop {\lim }\limits_{n \to \infty } \,\,\frac{{1\,\, + \,\,{2^3}\,\, + \,\,{3^3}\,\, + \,\,... + \,\,{n^3}}}{{{n^5}}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\lim\limits_{n \to \infty } \,\,\frac{{1\,\, + \,\,{2^4} + \,\,{3^4} + \,\,... + \,\,{n^4}}}{{{n^5}}}\,\, - \,\,\lim\limits_{n \to \infty } \,\,\frac{{1\,\, + \,\,{2^3}\,\, + \,\,{3^3}\,\, + \,\,... + \,\,{n^3}}}{{{n^5}}}

View answer and explanation

Correct option: D

\frac{1}{5}

Option D (

\frac{1}{5}

) is correct because it represents the difference between the integrals of x⁴ and 0, evaluated from 0 to 1.

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