series comparison and limit comparison test question

[crbrown91]

I can't think of an equation to compare the following equation to

The summation from 1 to infinity of (x+2)/(x+1)^3

any and all help would be appreciated
Thank you

 

[Deleted member 4993]

I can't think of an equation to compare the following equation to

The summation from 1 to infinity of (x+2)/(x+1)^3

any and all help would be appreciated
Thank you

\(\displaystyle \dfrac{x+2}{(x+3)^3} \ = \ \dfrac{1}{(x+3)^2} \ - \ \dfrac{1}{(x+3)^3}\)

 

[crbrown91]

I'm pretty new to series and comparison tests
How does this equation help me to compare to the other equation to find convergence or divergence?