Induction of $\sum_{k=1}^{n} (-1)^{n-k}k^2 = \frac{n(n+1)}{2}$ I'm trying to prove following statement through induction:
$\sum_{k=1}^{n} (-1)^{n-k}k^2 = \frac{n(n+1)}{2}$
I have only seen how to prove with induction when the variable $n$ is not included in the sum function. Like here (this statement is not correct, just to provide an example):
$\sum_{k=1}^{n} (-1)^{k}k^2 = \frac{n(n+1)}{2}$
It confuses me and I don't know how to proceed. Any advice?
Thank you.

$$\sum_{k=1}^n(-1)^{n-k}k^2=(-1)^n\sum_{k=1}^n(-1)^{-k}k^2=(-1)^n\sum_{k=1}^n(-1)^kk^2\\\sum_{k=1}^n(-1)^kk^2=(-1)^n\frac{n(n+1)}{2}$$
