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Mathematics
Problem
A power series
∑
n
=
0
∞
a
n
(
x
−
1
)
n
\sum_{n=0}^{\infty} a_n (x-1)^n
∑
n
=
0
∞
a
n
(
x
−
1
)
n
has radius of convergence
R
R
R
. A new series is formed by multiplying every coefficient by
7
7
7
, giving
∑
n
=
0
∞
7
a
n
(
x
−
1
)
n
\sum_{n=0}^{\infty} 7a_n (x-1)^n
∑
n
=
0
∞
7
a
n
(
x
−
1
)
n
. What is the radius of convergence of the new series?
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