Question

Express the following as the sum of two consecutive integers.
${19}^2$

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
${19}^2=({19}^2-1)/2+({19}^2+1)/2$
We know that
${19}^2=361$
By further calculation
$=(361-1)/2+(361+1)/2$
So we get
$180+181$