9231 P11 - Jun 2013 - Q5 - 9 marks
6390
Use the method of differences to show that \(\sum_{r=1}^{N} \frac{1}{(2 r+1)(2 r+3)}=\frac{1}{6}-\frac{1}{2(2 N+3)}\).
Deduce that \(\sum_{r=N+1}^{2 N} \frac{1}{(2 r+1)(2 r+3)}\lt \frac{1}{8 N}\).
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