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Mathematics
Problem
Consider the alternating series
∑
k
=
1
∞
(
−
1
)
k
+
1
k
3
k
\displaystyle \sum_{k=1}^{\infty} (-1)^{k+1}\frac{k}{3^{k}}
k
=
1
∑
∞
(
−
1
)
k
+
1
3
k
k
. What is the smallest integer
N
N
N
such that the partial sum
S
N
S_N
S
N
is guaranteed to approximate the series within
0.001
0.001
0.001
? a)
N
=
7
N=7
N
=
7
b)
N
=
8
N=8
N
=
8
c)
N
=
9
N=9
N
=
9
d)
N
=
6
N=6
N
=
6
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