Combining power series Use the power series representation to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.p(x)= 2x6 In (1 ? x)

Solution 31EStep 1:In this problem we have to find the power series of p(x) = (centered at ‘o’), and the interval of convergence of the new series.Given f(x) = ln(1-x) = - , for -1…………(1)Step 2: Given , p(x) = = 2, since from(1). = - , since Step 3: Now , we have to find out the interval of convergence of the new series. The new series is ; p(x) = -Use Ratio test to determine the interval of convergence.If and1. If L <1, converges.2. If L >1, diverges.3. If L=1, the test is inconclusive.