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Mathematics
Mathematics
Problem
For a real constant
α
\alpha
α
, examine the series
∑
n
=
0
∞
α
+
n
2
4
n
(
x
−
2
)
n
.
\sum_{n=0}^{\infty} \frac{\alpha+n^{2}}{4^{n}}\,(x-2)^{n}.
n
=
0
∑
∞
4
n
α
+
n
2
(
x
−
2
)
n
.
Determine the radius of convergence and the closed interval of
x
x
x
-values on which the series fails to converge.
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