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Mathematics
Problem
Determine all real numbers
x
x
x
for which the series
∑
n
=
1
∞
(
x
−
1
)
n
n
2
n
\displaystyle \sum_{n=1}^{\infty} \dfrac{(x-1)^{n}}{n\,2^{n}}
n
=
1
∑
∞
n
2
n
(
x
−
1
)
n
converges. a)
(
−
1
,
3
)
(-1,\,3)
(
−
1
,
3
)
b)
[
−
1
,
3
)
[-1,\,3)
[
−
1
,
3
)
c)
(
−
1
,
3
]
(-1,\,3]
(
−
1
,
3
]
d)
[
−
1
,
3
]
[-1,\,3]
[
−
1
,
3
]
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