The given series is C and choose sine series S=12sinα+1.32.4sin2α+1.3.52.4.6sin3α+⋯ ∴C+iS=1+12eiα+12.321.2e2iα+12.32.521.2.3e3iα+⋯ =1+12eiα+12(12+1)2!e2iα+12(12+1)(12+2)3!e3iα+⋯ =(1−eia)−1/2=(1−cosα−isinα)−1/2 =(2sin2α2−2isinα2cosα2)−1/2 =(2sinα2)−1/2[sinα2−icosα2]−1/2 =(2sinα2)−1/2[cos(π2−α2)−isin(π2−α2)]−1/2 =(2sinα2)−1/2[cosπ−α4+isinπ−α4]