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Mathematics
Problem
Determine all real numbers
x
x
x
for which the infinite series
∑
n
=
0
∞
(
2
x
)
n
\displaystyle \sum_{n=0}^{\infty} (2x)^{n}
n
=
0
∑
∞
(
2
x
)
n
converges, and express the sum as a closed-form function of
x
x
x
on that interval.
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