JEE Main 202225 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002 If limn→∞(n+1)k−1nk+1[(nk+1)+(nk+2)+…+(nk+n)]=33⋅limn→∞1nk+1⋅[1k+2k+3k+…+nk]\begin{aligned} &\text { If } \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] \end{aligned} If n→∞limnk+1(n+1)k−1[(nk+1)+(nk+2)+…+(nk+n)]=33⋅n→∞limnk+11⋅[1k+2k+3k+…+nk], then the integral value of k\mathrm{k}k is equal to _____________Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
