Hi
Shame on me for asking this but
$\displaystyle \bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2$
Do you multiply everything out before subtracting ?
I got the answer n+1 but it's wrong.
Hello JonesNo, not if you want the easiest method!
Note that each term has a common factor $\displaystyle \frac{n+1}{2}$, so take it out (not forgetting that it has to be squared):
$\displaystyle \bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2= \Big(\frac{n+1}{2}\Big)^2\Big((n+2)^2-n^2\Big)$
Even now, there's no need to multiply out. Use 'difference of two squares' in the second bracket.
Grandad