JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

\alpha>-1

and

\beta>-1

, then the value of

\lim \limits_{{n \rightarrow \infty}} n^{\beta-\alpha}\left(\frac{1^\alpha+2^\alpha+\ldots+n^\alpha}{1^\beta+2^\beta+3^\beta+\ldots . n^\beta}\right)

View answer and explanation

Correct option: A

\frac{\beta+1}{\alpha+1}

Option B (

\frac{{\alpha+1}}{{\beta+1}}

) is incorrect. The correct answer is A (

\frac{{\beta+1}}{{\alpha+1}}

) because it is found by evaluating the limit of the ratio of sums using integrals.

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