(a) Find a closed-form formula for the series 3(33) : 1 1'2 | 35:4 3:6 + . . .. For what values of a: does your formula work? (b) Let P(;r) be a function such that P(O) : 0 and PTI) : 3(3). Find a series formula for P(:c) by nding the antiderivative of each term in the series formula for 3(33). Determine the interval of 3: values Where P(;r) converges. (c) Find a closed form formula for P[:c) Does your answer from part (b) converge to this formula? For what .rvalues do you think this formula works? Check your reasoning by graphing the closed-form formula against several partial sums of the series you found in part (b). 111 (d) Let A = 1 i g + g 7 ? + . . .. Does the series converge? If so, What value does it converge to