9231 P12 - Nov 2014 - Q1 - 5 marks
6364
Given that
\(u_{k}=\frac{1}{\sqrt{2 k-1}}-\frac{1}{\sqrt{2 k+1}},\)
express \(\sum_{k=13}^{n} u_{k}\) in terms of \(n\).
Deduce the value of \(\sum_{k=13}^{\infty} u_{k}\).
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