Problem #PRU-100274

Prove that

(a) $1^{2} + 2^{2} + 3^{2} + \dots + n^{2} = \frac{1}{6} n (n + 1) (2 n + 1)$

(b) $1^{2} + 3^{2} + 5^{2} + \dots + (2 n - 1)^{2} = \frac{1}{3} n (2 n - 1) (2 n + 1)$ .

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