[Please excuse the screengrabs of the fomulae - I'll get around to learning TeX someday!] 1. The problem statement, all variables and given/known data Find the sum of this series (answer included - not the one I'm getting) 3. The attempt at a solution So I'm trying to sum this series as a telescoping sum. I decomposed the fraction and the partial sum collapses down to this: Then when I take the limit, the second term vanishes, leaving just the first term as the final value, i.e.: Needless to say 48/23 ≠ 3/23 I can't see what I'm doing wrong - I've triple-checked everything & must be misunderstanding something fundamentally speaking. The partial fraction decomposition is (to the best of my / Wolfram A's knowledge) correct. Can anyone point out my mistake(s)?