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Mathematics
Mathematics
Problem
Determine the least integer
N
N
N
such that the partial sum
S
N
=
∑
n
=
1
N
(
−
1
)
n
+
1
n
S_{N}=\displaystyle\sum_{n=1}^{N}\frac{(-1)^{n+1}}{n}
S
N
=
n
=
1
∑
N
n
(
−
1
)
n
+
1
approximates the entire series to within
0.001
0.001
0.001
. a)
N
=
1000
N=1000
N
=
1000
b)
N
=
999
N=999
N
=
999
c)
N
=
500
N=500
N
=
500
d)
N
=
998
N=998
N
=
998
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