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Mathematics
Problem
What is the smallest positive integer
N
N
N
such that the
N
N
N
th partial sum of
∑
n
=
1
∞
(
−
1
)
n
+
1
n
\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}
n
=
1
∑
∞
n
(
−
1
)
n
+
1
approximates the series’ sum with an absolute error less than
0.001
0.001
0.001
?
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