Induction/Alternating sum of squares/Exercise

Prove, by induction, that the formula

${}\sum _{k=1}^{n}(-1)^{k-1}k^{2}=(-1)^{n+1}{\frac {n(n+1)}{2}}\,$

holds for all ${}n\in \mathbb {N} _{+}$.

To solution