Limit, Sum, Fraction

Calculus Level 3

limnn+n2+n3++nn1n+2n+3n++nn \displaystyle \lim_{n\to\infty} \dfrac{n + n^2+ n^3 + \cdots + n^n}{1^n + 2^n + 3^n + \cdots + n^n}

What is the value of this limit?

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