N2008 P1 Q2

The \(n\)th term of a sequence is given by \(u_n=n(2n+1)\), for \(n\geq1\). The sum of the first \(n\) terms is denoted by \(S_n\). Use the method of mathematical induction to show that \(S_n=\frac16n(n+1)(4n+5)\) for all positive integers \(n\).[5]