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Mathematics
Mathematics
Problem
A power series
∑
n
=
0
∞
b
n
t
n
\displaystyle \sum_{n=0}^{\infty} b_n t^{n}
n
=
0
∑
∞
b
n
t
n
converges for
∣
t
∣
<
2
|t|<2
∣
t
∣
<
2
. For what real values of
x
x
x
does the series
∑
n
=
0
∞
b
n
(
3
x
−
1
)
n
\displaystyle \sum_{n=0}^{\infty} b_n\,(3x-1)^{n}
n
=
0
∑
∞
b
n
(
3
x
−
1
)
n
converge? Give your answer as an open interval.
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