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Mathematics
Problem
Consider the series
S
=
∑
k
=
1
∞
(
−
1
)
k
1
k
3
\displaystyle S=\sum_{k=1}^{\infty} (-1)^{k}\frac{1}{k^{3}}
S
=
k
=
1
∑
∞
(
−
1
)
k
k
3
1
. Using the partial sum
S
4
S_{4}
S
4
, give a numerical upper bound for
∣
S
−
S
4
∣
|S-S_{4}|
∣
S
−
S
4
∣
.
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