Question

Express the following as the sum of two consecutive integers.
${33}^2$

Answer 1

We know that
$n^2=(n^2-1)/2+(n^2+1)/2$ is the sum of two consecutive integers when $n$ is odd
${33}^2=({33}^2-1)/2+({33}^2+1)/2$
We know that
${33}^2=1089$
By further calculation
$=(1089-1)/2+(1089+1)/1$
So we get
$1088/2+1090/2$
$=544+545$