# Thread: I officially loathe infinite series...

1. ## I officially loathe infinite series...

Conditionally convergent, absolutely convergent or divergent?

$\sum^{\infty}_{n=1} \frac{12^n}{(n+1)8^{2n+1}}$

2. Positive series implies that the convergence is absolute, thus, prove that the series converges and you'll get absolute convergence.

3. Originally Posted by Krizalid
Positive series implies that the convergence is absolute, thus, prove that the series converges and you'll get absolute convergence.
So would I use

$\frac{1}{n+1}$

to do this?

4. Originally Posted by mollymcf2009
So would I use

$\frac{1}{n+1}$

to do this?
No, because it looks similar to the harmonic series term $\frac{1}n$ which would then suggest that the series diverges.

I would suggest comparing this to $\frac{12^n}{8^{2n}}=\left(\frac{3}{16}\right)^n$ which is geometric.