Mathematics · 2022
JEE Main · 25 July 2022, Shift 1 · Q27
If lim_n → ∞((n+1)^k-1)/(n^k+1)[(n k+1)+(n k+2)+…+(n k+n)] =33 · lim_n → ∞ 1/(n^k+1) ·[1^k+2^k+3^k+…+n^k], then the integral value of k is equal to \…
If $\displaystyle \lim _{n \rightarrow \infty}\frac{(n+1)^{k-1}}{n^{k+1}}[(n k+1)+(n k+2)+\ldots+(n k+n)]$
$$=33 \cdot \lim _{n \rightarrow \infty} \frac{1}{n^{k+1}} \cdot\left[1^k+2^k+3^k+\ldots+n^k\right],
$$
then the integral value of k is equal to \_\_\_\_.
Official answer
5
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.