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Mathematics
Problem
The series
∑
k
=
2
∞
(
−
1
)
k
ln
k
k
2
\displaystyle\sum_{k=2}^{\infty} (-1)^{\,k}\dfrac{\ln k}{k^{2}}
k
=
2
∑
∞
(
−
1
)
k
k
2
ln
k
converges. Using the first four nonzero terms to approximate its sum, which of the following is the largest possible magnitude of the error of this approximation? a)
0.064
0.064
0.064
b)
0.040
0.040
0.040
c)
0.050
0.050
0.050
d)
0.045
0.045
0.045
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