Question: Prove each of the following for all n> by the Principal of Mathematical Induction.

a). \[{{1}^{2}}+{{3}^{2}}+{{5}^{2}}...+{{(2n-1)}^{2}}=\frac{n(2n-1)(2n+1)}{3}\]

b). \(1*3+2*4+3*5+...+n(n+2)=\frac{n(n+1)(2n+7)}{6}\)