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Mathematics
Mathematics
Problem
Determine the least integer
n
n
n
such that the partial sum
S
n
=
∑
k
=
1
n
(
−
1
)
k
+
1
1
k
S_{n}=\sum_{k=1}^{n} (-1)^{k+1}\frac{1}{k}
S
n
=
∑
k
=
1
n
(
−
1
)
k
+
1
k
1
approximates the total sum of the series to within
0.0005
0.0005
0.0005
.
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