# Dice games, part 2

Calculus Level 5

Let $$E_{n,p}$$ be the expected value of rolling an $$n$$-sided die $$p$$ times and choosing the greatest number shown.

The limit $$\displaystyle\lim_{n \to \infty} \frac{E_{n,20}}{E_{n,30}}$$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are relatively coprime positive integers. Find $$a+b$$.

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