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# 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 Lakshya Sinha
10 months, 3 weeks ago

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