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

(xi)

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

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(xi)

(33)+(43)+(53)+⋯+(n+23)=(n+34)\dbinom{3}{3} + \dbinom{4}{3} + \dbinom{5}{3} + \cdots + \dbinom{n+2}{3} = \dbinom{n+3}{4}

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