# Let's do some calculus! (18)

Calculus Level 4

$\lim_{n \to \infty} {\dfrac{\left(1^{a}+2^{a}+3^{a}+ \cdots + n^{a}\right)}{{\left(n+1\right)}^{a-1} \left[\left(na+1\right) + \left(na+2\right) + \left(na+3\right) + \cdots + \left(na+n\right) \right]}} = \dfrac{1}{60}$

Find $$a \in \mathbb{R^+}$$ that satisfies the equation above.