Theory of Intelligence
11TH•Mathematics•Mathematical Inductions And Binomial Theorem•Question 1

(vi)

Use mathematical induction to prove the following formulae for every positive integer $n$.

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(vi)

11×2+12×3+13×4+⋯+1n(n+1)=1−1n+1\dfrac{1}{1\times 2} + \dfrac{1}{2\times 3} + \dfrac{1}{3\times 4} + \cdots + \dfrac{1}{n(n+1)} = 1 - \dfrac{1}{n+1}

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