It is given that \(\sum\limits_{r=-1}^n r^2\) can be written in the form \(pn^3+qn^2+rn+s\), where \(p,q,r\) and \(s\) are numbers. By setting \(n=-1,0,1\) and \(2\), obtain four equations that must be satisfied by \(p,q,r\) and \(s\) and hence show that \[ \sum_{r=0}^n r^2=\frac{1}{6}n(n+1)(2n+1). \] Given that \(\sum\limits_{r=-2}^n r^3\) can be written in the form \(an^4+bn^3+cn^2+dn+e\), show similarly that \[ \sum_{r=0}^n r^3=\frac{1}{4}n^2(n+1)^2. \]