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Mathematics
Mathematics
Problem
Consider the series
∑
n
=
1
∞
(
−
1
)
n
−
1
1
3
n
\displaystyle\sum_{n=1}^{\infty}(-1)^{n-1}\dfrac{1}{3n}
n
=
1
∑
∞
(
−
1
)
n
−
1
3
n
1
. Determine the smallest integer
N
N
N
such that the absolute error
∣
S
N
−
S
∣
|S_N-S|
∣
S
N
−
S
∣
between the
N
N
N
th partial sum
S
N
S_N
S
N
and the exact sum
S
S
S
of the series is less than
0.01
0.01
0.01
.
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