JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 27

If $\displaystyle\lim_{n\to\infty}\frac{(n+1)^{k-1}}{n^{k+1}}\left[(nk+1)+(nk+2)+\dots+(nk+n)\right]=33\cdot\lim_{n\to\infty}\frac1{n^{k+1}}\cdot\left[1^k+2^k+3^k+\dots+n^k\right]$, then the integral value of k is equal to ______.