9231 P1 - Nov 2008 - Q9 - 10 marks
6472
Use induction to prove that
\(\sum_{n=1}^{N} \frac{4 n+1}{n(n+1)(2 n-1)(2 n+1)}=1-\frac{1}{(N+1)(2 N+1)}\)
Show that
\(\sum_{n=N+1}^{2 N} \frac{4 n+1}{n(n+1)(2 n-1)(2 n+1)}\lt \frac{3}{8 N^{2}} .\)
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