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![$ \lim_{n \to \infty} \sqrt[n]{|a_n|} < 1 \implies \sum_{n=1}^{\infty} a_n \text{ is convergent}$](/tpl/images/1378/6612/0c8af.png)
![$\lim_{n \to \infty} \sqrt[n]{\left(\dfrac{1}{4} \right)^{n}} = \lim_{n \to \infty} \dfrac{1}{4} = \dfrac{1}{4} < 1$](/tpl/images/1378/6612/3e011.png)
and the ratio is also 
such that 
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∑_(n=1)^∞▒〖( 1/2 )〗^2n...
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