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

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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestPlease post the solution and the next problem(not soo hard please) – Brilliant Member · 1 year, 7 months ago

Log in to reply

Are the \(a_n\)'s distinct? – Brilliant Member · 1 year, 7 months ago

Log in to reply

– Lakshya Sinha · 1 year, 7 months ago

It can be anythingLog in to reply