Question 772378
Interesting question!
Try to generalize and try the same process.


Three consecutive integers, n, n+1, n+2.



SQUARE THE SECOND INTEGER.
{{{(n+1)^2}}}
{{{n^2+2n+1}}}


MULTIPLY THE FIRST AND THIRD INTEGERS.
{{{n(n+2)}}}
{{{n^2+2n}}}


FIND THE DIFFERENCE BETWEEN THOSE TWO RESULTS.
{{{(n^2+2n+1)-(n^2+2n)=n^2+2n+1-n^2-2n=n^2-n^2+2n-2n+1=0+0+1=1}}}


n can be ANY integer.  The process will still work.