If lim n→∞ [(n+1)^(k−1)/n^(k+1)] Σ(nk+r) = 33 lim n→∞... | Limits | JEE Main

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JEE MAIN 2022

25-07-22 S1

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If $\lim _{n \rightarrow \infty} \frac{(n+1)^{k-1}}{n^{k+1}}[(n k+1)+(n k+2)+\ldots+(n k+n)]=33 . \lim _{n \rightarrow \infty} \frac{1}{n^{k+1}}\left[1^k+2^k+3^k+\ldots . .+n^k\right]$, then the integral value of k is equal to $\_\_\_\_$

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