The series \(\sum \frac{{{{\left( {n!} \right)}^2}}}{{\left( {2n} \right)!}}{x^{2n}}\) converges if

1
x ≤ -2 and x ≥ 2
2
-2 ≤ x ≤ 2
3
-2 < x < 2
4
x < -2 and x > 2

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