Convergence/Divergence of an infinite series

[rdioface]

Homework Statement

Prove the convergence or divergence of the series \Sigma(\frac{n}{2n+3})^{2} using the Direct Comparison Test.

Homework Equations

If series A converges and every term in series B is less than the corresponding term in series A, then series B converges.
If series C diverges and every term in series D is greater than the corresponding term in series C, then series D diverges.

The Attempt at a Solution

I can't think of anything useful to compare it to. Turning either the top or the bottom to 1 doesn't yield anything useful, nor does it behave as a p-series.

 

[tiny-tim]

hi rdioface!

(use "left(" and "right)" to automatically get latex brackets the right size )

always try to simplify by getting things as close to 1 as possible …

in this case, try divdiding top and bottom by n