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Mathematics
Problem
The partial sum
S
7
S_{7}
S
7
of the series
∑
k
=
1
∞
(
−
1
)
k
+
1
1
k
2
\sum_{k=1}^{\infty} (-1)^{k+1}\frac{1}{k^{2}}
∑
k
=
1
∞
(
−
1
)
k
+
1
k
2
1
is
0.947832
0.947832
0.947832
. How many decimal places in this approximation are guaranteed to be correct?
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