N2009 P1 Q5

N2009 P1 Q5

Junior College 2
8 marks

Use the method of mathematical induction to prove that \(\displaystyle\sum_{r=1}^{n}r^2=\frac16n(n+1)(2n+1)\).[4]

Find \(\displaystyle\sum_{r=n+1}^{2n}r^2\), giving the answer in fully factorised form.[4]

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Answer:\(\displaystyle\sum_{r=n+1}^{2n}r^2=\frac16n(2n+1)(7n+1)\).

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