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Mathematics
Problem
The alternating series
∑
n
=
1
∞
(
−
1
)
n
+
1
n
2
\displaystyle\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n^{2}}
n
=
1
∑
∞
n
2
(
−
1
)
n
+
1
converges to
S
=
π
2
12
S=\dfrac{\pi^{2}}{12}
S
=
12
π
2
. Determine the smallest integer
N
N
N
such that
∣
S
−
S
N
∣
<
0.0005
|S-S_N|<0.0005
∣
S
−
S
N
∣
<
0.0005
. a)
32
32
32
b)
44
44
44
c)
45
45
45
d)
43
43
43
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