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Mathematics
Mathematics
Problem
Let
S
=
∑
n
=
1
∞
(
−
1
)
n
+
1
1
n
3
S=\displaystyle\sum_{n=1}^{\infty} (-1)^{\,n+1}\dfrac{1}{n^{3}}
S
=
n
=
1
∑
∞
(
−
1
)
n
+
1
n
3
1
. What is the least integer
N
N
N
such that the absolute error
∣
S
−
S
N
∣
|S-S_N|
∣
S
−
S
N
∣
in using the
N
N
N
th partial sum
S
N
S_N
S
N
is less than
0.0005
0.0005
0.0005
? a)
N
=
13
N=13
N
=
13
b)
N
=
12
N=12
N
=
12
c)
N
=
14
N=14
N
=
14
d)
N
=
11
N=11
N
=
11
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