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Mathematics
Problem
Determine whether the series
∑
n
=
0
∞
(
−
3
)
n
+
1
2
2
n
\displaystyle \sum_{n=0}^{\infty} \frac{(-3)^{\,n+1}}{2^{\,2n}}
n
=
0
∑
∞
2
2
n
(
−
3
)
n
+
1
converges. If it does, state its sum.
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