Prove by induction that (Sigma_{r=1}^{n} r^{2}=frac{1}{6} n(n+1)(2 n+1)). Deduce formulae for (1 cdot 1+2 cdot 3+3 cdot
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Prove by induction that \(\Sigma_{r=1}^{n} r^{2}=\frac{1}{6} n(n+1)(2 n+1)\).
Deduce formulae for
\(1 \cdot 1+2 \cdot 3+3 \cdot 5+4 \cdot 7+\cdots+n(2 n-1)\) and \(1^{2}+3^{2}+5^{2}+\cdots(2 n-1)^{2}\).
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