Question

Express the following as the sum of two consecutive integers.
${47}^2$

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
${47}^2=({47}^2-1)/2+({47}^2+1)/2$
We know that
${47}^2=2209$
By further calculation
$=(2209-1)/2+(2209+1)/1$
So we get
$2208/2+2210/2$
$=1104+1105$