# Limits And Summations!

Calculus Level 5

$\large L = \lim_{n \to \infty} \dfrac{1}{\sqrt[n]{n!}} \log_a \left( \displaystyle \sum_{k=1}^{a^n} (1+k)^{a^{-n}} \right)$

Let $$a>1$$ be any positive integer, find the value of $$\lfloor 100L \rfloor$$.

 Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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