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

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

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

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

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## Comments

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TopNewestPlease post the solution and the next problem(not soo hard please) – Svatejas Shivakumar · 1 year, 5 months ago

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Are the \(a_n\)'s distinct? – Svatejas Shivakumar · 1 year, 5 months ago

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– Lakshya Sinha · 1 year, 5 months ago

It can be anythingLog in to reply