Telescoping rational sums
Telescoping rational sums
5 marks
Tim Gan Math Original
Find \(\sum_{r=3}^{n}\frac1{r^2-1}\) in terms of \(n\).[5]
Take \(n\) to be an integer with \(n\ge 3\).
Solution:
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Answer:\(\frac5{12}-\frac1{2n}-\frac1{2(n+1)}\)
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