# Proof Contest Day 8

Suppose that $$a_n > 0$$ for each $$n$$ and that $$\displaystyle \lim _{ n\to \infty }{ \dfrac { { a }_{ n+1 } }{ { a }_{ n } } } =l$$. Prove that

$\large{\lim _{ n\to \infty }{ \sqrt [ n ]{ { a }_{ n } } } =l}.$

Note by Department 8
2 years, 6 months ago

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- 2 years, 6 months ago

Are the $$a_n$$'s distinct?

- 2 years, 6 months ago

It can be anything

- 2 years, 6 months ago