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Induction/Alternating sum of squares/Exercise
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Prove, by induction, that the formula
∑
k
=
1
n
(
−
1
)
k
−
1
k
2
=
(
−
1
)
n
+
1
n
(
n
+
1
)
2
{\displaystyle {}\sum _{k=1}^{n}(-1)^{k-1}k^{2}=(-1)^{n+1}{\frac {n(n+1)}{2}}\,}
holds for all
n
∈
N
+
{\displaystyle {}n\in \mathbb {N} _{+}}
.
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