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Mathematics
Mathematics
Problem
Determine the radius of convergence of the series
∑
n
=
0
∞
(
2
n
)
!
(
n
!
)
2
(
x
−
4
)
n
\displaystyle\sum_{n=0}^{\infty} \frac{(2n)!}{(n!)^{2}}\,(x-4)^{n}
n
=
0
∑
∞
(
n
!
)
2
(
2
n
)!
(
x
−
4
)
n
. a)
1
2
\dfrac{1}{2}
2
1
b)
1
4
\dfrac{1}{4}
4
1
c) 4 d) 1
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