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Mathematics
Mathematics
Problem
Consider the series
∑
k
=
1
∞
(
−
1
)
k
+
1
k
2
\displaystyle \sum_{k=1}^{\infty} \dfrac{(-1)^{k+1}}{k^{2}}
k
=
1
∑
∞
k
2
(
−
1
)
k
+
1
. What is the smallest positive integer
n
n
n
such that the absolute error when
S
n
S_n
S
n
is used to approximate the infinite sum is less than
0.0005
0.0005
0.0005
? a)
63
63
63
b)
45
45
45
c)
44
44
44
d)
43
43
43
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