Simplifying an Infinite Series with Partial Fractions

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The discussion focuses on simplifying the infinite series Σ_{n=1}^{∞} (1/((3n-2)(3n+1))) using partial fractions. The series is expressed as (1/3) / (3n-2) - (1/3) / (3n+1), which reveals that many terms will cancel out. Participants are encouraged to identify the finite number of terms that do not cancel by writing out the partial fraction expansion for the first few values of n. Observing these terms helps in recognizing the emerging pattern. The goal is to simplify the series further by determining the non-canceling terms.
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\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?
 
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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.
 

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