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Mathematics
Mathematics
Problem
The series
∑
n
=
1
∞
(
−
1
)
n
+
1
1
n
3
\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{1}{n^{3}}
n
=
1
∑
∞
(
−
1
)
n
+
1
n
3
1
converges. Determine the least positive integer
N
N
N
such that the partial sum
S
N
S_N
S
N
approximates the infinite series to within
0.0005
0.0005
0.0005
.
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