Series problem (show work)?

Question

Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.

E,n=1, 2/(n^(2) +4n +3)

Answer 1

This is convergent, with sum 5/6. Do a partial fraction decomposition, so the terms are written as (1/(n+1) - 1/(n+3)). Note that this is telescopic: (1/2 - 1/4) + (1/3 - 1/5) + (1/4 - 1/6) + ... Only 1/2 + 1/3 remain, and all other terms cancel.

Technically, you may argue this way: since the series is absolutely convergent (all terms are positive, so the convergence is absolute), you can rearrange as follows.
1/2 + 1/3 + (1/4 - 1/4) + (1/5 - 1/5) + ... = 5/6.

Answer 2

it's convergent, just trust me. why would i do the problem and then take the time to type it in here just so you can cheat and copy my answer. i did your problem i told you the answer. now figure out how i did it yourself.