(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The following series is a telescopic series. Find the exact sum of the series by performing a partial fraction decomposition and generalizing the formula for the nth partial sum S_{n}.

2. Relevant equations

3. The attempt at a solution

3n + 2 = A(n+1)(n+2) + B(n)(n+2) + C(n)(n+1)

n = 0 → 2 = 2A → A = 1

n = -1 → -1 = -B → B = 1

n = -2 → -4 = 2C → C = -2

(3n+2)/(n(n+1)(n+2)) = 1/n + 1/(n+1) + 2/(n+2)

=> S_{n}= ... = 1 + 1/2 + 1/3 + ... + 1/n + 2/3 + 2/5 + 2/7 + ... + 1/(2n + 1)

I don't see the terms cancel. Did i do something wrong?

Thanks

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# Homework Help: Recursive sequence terms don't cancel

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