How do you find radius of convergence of the power series sum n=0 to infinity (1/2^n)*x^n

Question : How do you find radius of convergence of the power series \[\sum_{n=0}^{\infty}{\frac{1}{2^n}x^n}\] Solution : We know that radius of convergence of the power series \[\sum_{n=0}^{\infty}{a_nx^n}\] is given as\[ R=limit_{n\rightarrow\ \infty}\ \frac{a_{n+1}}{a_n}\] Since for the power series \[\sum_{n=0}^{\infty}{\frac{1}{2^n}x^n}\] \[a_n=\frac{1}{2^n},\…

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