Simplifying an Infinite Series with Partial Fractions

[razored]

$$\Sigma_{n=1}^{ \infty} \frac{1}{(3n-2)(3n+1)}$$ I simplified it to partial fractions to (1/3) / (3n-2) - (1/3) / (3n+1) Now what?

 

[Dick]

An infinite number of terms cancel and a finite number of terms don't. Figure out which ones don't. Start writing out terms in the partial fraction expansion for n=1,2,3,4,5... if you need to. You should see the pattern pretty quickly.