summation - 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.

Answer

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