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Mathematics
Problem
Explain why the alternating series
∑
n
=
1
∞
(
−
1
)
n
−
1
1
n
2
\displaystyle\sum_{n=1}^{\infty}(-1)^{n-1}\dfrac{1}{n^{2}}
n
=
1
∑
∞
(
−
1
)
n
−
1
n
2
1
satisfies the conditions required to guarantee that the absolute error of a partial sum is bounded by the magnitude of the next term.
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