(a) Show that the series Michal\") n=1 converges for every 2 a mar for any nonzero integer m and that 9(0) =0. Hint: combine the fractions and use the Absolute Convergence Test. (b) The function 1 1 1 f(z)=;+z(zn7r+z+n7r) n=1 is thus well-dened for every z 3% mar for any integer m. Show that lim 216(2) = 1: f(Z) = f(Z), f(Z-l-7l') = 10(2): f(''/2) = 0: (1) 2)0 with the middle identities holding whenever either side is dened (z % mm for any integer m). Hint: use partial sums for the third equality; the other three are easy. (c) What is the \"simplest\" function that satises all identities in (1)? (answer only) TF2 00 1 Note: This all leads to E E = K; see the solutions for more details. n21