I need help on these 6 math problems:

Find a power series representation of f. Use a gemoetric series and properties of power series. 4 f (x) = 5(1 - x)2 (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter the series such that the first term is defined at k = 1.)For the given function. nd the following 81:2 x+4 x} = (a) Use a geometric series to represent each function as a power series centered at 0. i k=0 (1)) Determine the radius of convergence R and the interval of convergence. (Use symbolic notation and fractions where needed. For the second part of the question, give your answer as an interval in the form [*,*). Use the symbol 00 for innity. U for combining intervals. and an appropriate type of parenthesis "(" ")". "L" or "J" depending on whether the interval is open or closed.) IE For the given function, find the following X f(x) = 1 + x6 (a) Use a geometric series to represent each function as a power series centered at 0. *= 0 (b) Determine the radius of convergence R and the interval of convergence. (Use symbolic notation and fractions where needed. For the second part of the question, give your answer as an interval in the form (*,*). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(" ")", "[" or "]" depending on whether the interval is open or closed.) R = X EFor the given function, find the following 12 f (x) = x +6 (a) Use a geometric series to represent each function as a power series centered at 0. (b) Determine the radius of convergence R and the interval of convergence. (Use symbolic notation and fractions where needed. For the second part of the question, give your answer as an interval in the form (*,*). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(" ")", "[" or "]" depending on whether the interval is open or closed.) R = X EFor the given function. nd the following 1 1+):6 x) = (a) Use a geometric series to represent each function as a power series centered at 0. (b) Determine the radius of convergence R and the interval of convergence. (Use symbolic notation and fractions where needed. For the second part of the question. give your answer as an interval in the form [*,*). Use the symbol oo- for innity. U for combining intervals. and an appropriate type of parenthesis "(" ")". "L" or " " depending on whether the interval is open or closed.) m: Find the radius of convergence and the interval of convergence of the series ('%)k kzl (Use symbolic notation and fractions where needed. For the second part of the question, give your answer as an interval in the form (*,*]. Use the symbol on for innity, U for combining intervals, and an appropriate type of parenthesis "(" "j", "[" or "J" depending on whether the interval is open or closed. If the series only converges at a number a, write the interval of convgergence as the interval from a to a.)