Determine the limit of $\frac1n \sum\limits_{i=1}^n i^\frac{1}{i}$ as ${n \to \infty}$ .

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How should I proceed? Should I count the sum upto infinity first and then proceed with the limit? Then again I can't even find the sum. Any help

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If $\{a_n\} \to a$ then $\frac {a_1+a_2+...+a_n} {n} \to a$. Apply this with $a_n =n^{1/n}$ (and $a=1$).