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Mathematics
Problem
For the series
∑
k
=
1
∞
3
k
(
x
−
1
)
k
k
\displaystyle\sum_{k=1}^{\infty} \frac{3^{k}(x-1)^{k}}{k}
k
=
1
∑
∞
k
3
k
(
x
−
1
)
k
, determine its interval of convergence. a)
(
2
3
,
4
3
]
(\tfrac{2}{3},\,\tfrac{4}{3}]
(
3
2
,
3
4
]
b)
(
2
3
,
4
3
)
(\tfrac{2}{3},\,\tfrac{4}{3})
(
3
2
,
3
4
)
c)
[
2
3
,
4
3
)
\left[\tfrac{2}{3},\,\tfrac{4}{3}\right)
[
3
2
,
3
4
)
d)
(
−
1
3
,
1
3
)
(-\tfrac{1}{3},\,\tfrac{1}{3})
(
−
3
1
,
3
1
)
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