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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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Please post the solution and the next problem(not soo hard please) Svatejas Shivakumar · 10 months, 2 weeks ago

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Are the \(a_n\)'s distinct? Svatejas Shivakumar · 10 months, 3 weeks ago

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@Svatejas Shivakumar It can be anything Lakshya Sinha · 10 months, 3 weeks ago

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