Some sums:

\[\sum_{r=1}^nr={\scriptsize\frac{1}{2}}n(n+1)\] \[\sum_{r=1}^nr^2={\scriptsize\frac{1}{6}}n(n+1)(2n+1)\] \[\sum_{r=1}^nr^3={\scriptsize\frac{1}{4}}n^2(n+1)^2\] \[\sum_{r=1}^nr^4={\scriptsize\frac{1}{30}}n(n+1)(2n+1)(3n^2+3n-1)\] \[\sum_{r=1}^nr^5={\scriptsize\frac{1}{12}}n^2(n+1)^2(2n^2+2n-1)\]