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Mathematics
Problem
A power series is given by
∑
n
=
0
∞
c
n
(
x
−
5
)
n
.
\displaystyle \sum_{n=0}^{\infty} c_n\,(x-5)^{n}.
n
=
0
∑
∞
c
n
(
x
−
5
)
n
.
Explain, in one or two sentences, why replacing each coefficient
c
n
c_n
c
n
by
∣
c
n
∣
|c_n|
∣
c
n
∣
does not affect the series’ radius of convergence.
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