A calculus problem by Akshat Sharda

Calculus Level 5

For \(k\in \mathbb{R}-\{-1\}\), \[\displaystyle \lim_{n\to \infty} \dfrac{ (n+1)^{1-k} \displaystyle \sum^{n}_{j=1} j^k}{\displaystyle \sum^{n}_{j=1} (nk+j)}=\dfrac{1}{60} \]

Find \(k\).

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