# Thread: absolutely converging or diverging?

1. ## absolutely converging or diverging?

heres the problem:
converging absolutely or diverging?

http://img525.imageshack.us/img525/2296/35297847wb1.png

I want to say that it diverges, but its said that it is absolutely convergent!

i was givin the hint of: http://img254.imageshack.us/img254/813/50083391wc0.png

however, what happened to the 3^n and also is the hint implying the divergence test?

i'm very new to the ratio test. this may be used here also.

thanks.

2. Originally Posted by rcmango
heres the problem:
converging absolutely or diverging?

http://img525.imageshack.us/img525/2296/35297847wb1.png

I want to say that it diverges, but its said that it is absolutely convergent!

i was givin the hint of: http://img254.imageshack.us/img254/813/50083391wc0.png

however, what happened to the 3^n and also is the hint implying the divergence test?

i'm very new to the ratio test. this may be used here also.

thanks.
yes, use the ration test

basically: $\displaystyle \sum a_n$ converges absolutely if $\displaystyle \lim \left| \frac {a_{n + 1}}{a_n} \right| < 1$, diverges if $\displaystyle \lim \left| \frac {a_{n + 1}}{a_n} \right| > 1$ and the ratio test gives no information if $\displaystyle \lim \left| \frac {a_{n + 1}}{a_n} \right| = 1$