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

(iii)

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

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(iii)

2+(2+5)+(2+5+8)+⋯+n2(3n+1)=n4(n+1)22 + (2+5) + (2+5+8) + \cdots + \dfrac{n}{2}(3n+1) = \dfrac{n}{4}(n+1)^2

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