Find the interval of convergence

Question

Find the interval of convergence for the power series

∑n=1∞ ( 2^n / n )(x^n)

Give your answer using interval notation. If you need to use  INF. If there is only one point in the interval of convergence, the interval notation is [a]. For example, if 0 is the only point in the interval of convergence, you would answer with [0].

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Answer 1

Use the ratio test to show that the interval of convergence is (-.5,.5).