How to solve this question of calculus?

(4 marks) Maddison and Madeline ask you to consider the power series i0: \"7)\" (1) nl n5\" (a) Maddison asks you to find the open interval of convergence I = (a, b) for the power series (1) and to enter the values of a and b in the boxes below: a= ID. b= JD. (b) Now, let f(a) = > (x - 7)n n5n for a in I (this is the interval found in part (a)). Madeline asks you to explain n=1 briefly in words why f' ( 20 ) = (2 - 7) (2 - 7) 2 (x - 7)n-1 + + + . . . - 52 + .. . 53 (2) for all x in I. (Note that the question continues below this essay box. Please scroll down.) 20 Q Equation Editor A . A- Ix BIUS X X Styles Font Size Words: 0Io. Find the sum 5 of the series (2): Redo (KW) S: .B. (d) Maddison and Madeline suggest that by integrating your result in part (c), you can find f(:c). Enter your result by making sure to find the constant of integration. f($)= D- Explain briefly in the box below how you found the constant of integration. (Note that this essay box will be marked only if your answer for f($) is wrong.) E Q E ESE?\" Words: 0 A