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Mathematics
Problem
For the series
∑
n
=
1
∞
(
−
1
)
n
+
1
2
3
n
\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{2}{3^{n}}
n
=
1
∑
∞
(
−
1
)
n
+
1
3
n
2
, let
S
3
S_3
S
3
denote the sum of the first three terms. (a) Calculate an interval that is guaranteed to contain the exact value of the infinite series. Provide your answer in exact fractional form.
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