The series \(\sum {u_n} = \frac{{{x^{2n}}}}{{\left( {n + 1} \right)\sqrt n }}\) converges for only 

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

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