Which Convergence Test to Use for ∑(k(k+2))/(k+3)^2 in Calculus?

[mickellowery]

Homework Statement

∑(k(k+2))/(k+3)^2 I honestly have no idea where to start with this I was going to try a ratio test but I wasn't sure if it would be (k+1)(k+3)/(k+4)²*(k+3)²/(k(k+2)

Homework Equations

3. The Attempt at a Solution

 

[Dunkle]

What is the limit as k goes to infinity of

\frac{k(k+2)}{(k+3)^{2}} ?

What does this tell you?

 

[physicsman2]

Big Hint: Going off of what Dunkle said, use Divergence Test.

 

[mickellowery]

Yea I was trying my hardest to make this problem way harder than it needed to be. Thanks a lot for your help.