Question

Does the series converge or diverge.
Use ratio test or root test.

Answer 1

\[a_{1}=1, a_{n+1}=\frac{ 1+\ln(n) }{ n}a _{n}\]

Answer 2

whats stopping you from using ratio test ?

Answer 3

http://gyazo.com/1688af58da902d5b193507ae8862a768

Answer 4

I dont know what to do with the an in an+1

Answer 5

take the ratio and it goes away

Answer 6

What would an be then?

Answer 7

doesn't matter

\[\large \lim\limits_{n\to \infty }\left|\dfrac{a_{n+1}}{a_n}\right| =\lim\limits_{n\to \infty }\left|\dfrac{\frac{1+\ln n}{n}a_n}{a_n}\right| = \lim\limits_{n\to \infty }\left|\dfrac{1+\ln n}{n}\right| \]

Answer 8

wouldn't it just be infinity over infinity then?

Answer 9

yes you may use L'hopital rule

Answer 10

Okay, so it would be 1/n, which be equal 0, so the series is convergent?

Answer 11

Yep!

Answer 12

THANKS SO MUCH! :D

Answer 13

yw