Plz help me to do question number 5 only step by step

no n _ (4) Compute the radius of convergence: 2 ne I n=1 7%. Answer: R = 1. :r (1+x2)3' (1)\"'1n(n+1) 2a-] f\": ' (5) Find a power series expansion for f(:r:) = Answer: f(:r) = 2 n=1 DO m2n+1 (6) Show that the power series y(:r) = Z W is a solution of the differential equation n=0 ' y"(:r) y(:r) = 0. Note that y(0) = 0. Can you nd another solution, 3(1):) say, with 3(0) = 4. Hint: If you differentiate y(m) twice, you will get the same series. Do it so that you see it! a:>1 R T? +1 11: Answer: L = 1. (telescoping series + Abel's theorem!) 2 m 1 1 (7) Compute the limit: L = lim ( ) 35\". 1 _ m _16' (8) Find a power series representation for f (1r)