9231 P13 - Nov 2012 - Q3 - 5 marks
6512
Let \(S_{N}=\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\ldots+\frac{N}{(N+1)!}\). Prove by mathematical induction that, for all positive integers \(N\),
\(S_{N}=1-\frac{1}{(N+1)!} .\)
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