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I have a question about the february 2004 midterm practise exam.

For #2b, the series is a telescoping series so we need to find the nth partial sum.

Why does Sn stop at n=n-1? Why doesn't Sn stop at n=n+2?

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It does not matter, since lim(s_{n}) is the same as lim(s_{n+2}) as n goes to infinity. In other words, if you use s_{n+2} and you will get the same answer.