1 00 Use the geometric series f(x) = m = 2 xk, for |x|

Use the geometric series f(x) = x , for < 1, to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series. Which of the following is the power series representation for g(x)? 00 7 k = OX The interval of convergence of the new series is (Simplify your answer. Type your answer in interval notation.) 7k