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What is the radius of convergence for the series $\sum _{ n=1 }^{ \infty }{ \cfrac { { \left( x-1 \right) }^{ 2n } }{ { 4 }^{ n } } } $?

A

$1$

B

$\cfrac { 1 }{ 2 } $

C

$2$

D

$\cfrac { 1 }{ 4 } $

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