Math 2414 Name: Operations on Power Series 1. Find a power series representation for the function f(x) = 5 and determine the 1 + 3x radius of convergence. 2. Find a power series representation for the function f(x) =- 8 - 23 3 and determine the radius of convergence.3. (40 points) (a) Find the power series for 1 1+ 22 and its radius of convergence. (b) Use part (a) to find a power series for (1 + 72)2 and state its radius of convergence. (c) Use part (b) to find the exact sum of the series (-1)"-In n=1 272 (d) Use part (a) to find a power series for a tan z and find its interval of convergence. (e) Use part (d) to find the exact sum of the series C (-1)2-1 n=1 3" (2n - 1)