$ (k+1)[k/2 + 1] = [(k+1)(k+2)] / 2 $
can anyone explain why the factorization becomes $ [(k+1)(k+2)] / 2 $
$ (k+1)[k/2 + 1] = [(k+1)(k+2)] / 2 $
can anyone explain why the factorization becomes $ [(k+1)(k+2)] / 2 $
Answer to the revised question. Observe that the factor $\frac{k}{2}+1=\frac{k+2}{2}$ and the other one is the same on both sides.
I assume $k=2$ is a typo for $k+2$, and trust you to work out why $(k/2)+1=(k+2)/2$.