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Mathematics
Problem
Determine whether the infinite series
∑
n
=
1
∞
5
⋅
2
n
−
1
3
n
\displaystyle \sum_{n=1}^{\infty} \frac{5\cdot 2^{\,n-1}}{3^{\,n}}
n
=
1
∑
∞
3
n
5
⋅
2
n
−
1
converges, and if it does, find its sum in simplest rational form.
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