$\lim\limits_{n\rightarrow\infty}\root n\of{a_n}=\lim\limits_{n\rightarrow\infty} {a_{n+1}\over a_n}$

Asked Jul 28 '13 at 03:03

Active Jul 28 '13 at 03:03

Viewed 123 times

Let $(a_n)$ a sequence of positive terms, show that if $\lim\limits_{n\rightarrow\infty} {a_{n+1}\over a_n}$ exists, then so does $\lim\limits_{n\rightarrow\infty}\root n\of{a_n}$ and the two limits are equal.

asked Jul 28 '13 at 03:03

Roiner Segura Cubero

3,923

I suggest that you dont use too much math script in your question title. It makes things troublesome. – Vishesh Jul 28 '13 at 03:11

$\lim\limits_{n\rightarrow\infty}\root n\of{a_n}=\lim\limits_{n\rightarrow\infty} {a_{n+1}\over a_n}$

0 Answers0