| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2012 |
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| Session | November |
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| Topic | Proof by induction |
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3 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 \(N\),
$$S _ { N } = 1 - \frac { 1 } { ( N + 1 ) ! }$$