Question

4. Find a power series representation for each of the following functions. Give the radius of convergence. a) (1 + r) b) (1 +2452 c) In(1 + 3.rº)

Answer 1

4) c) We know 1961+ 4) -- Chan nti 24" 0 converges for itki In(1+30 In our case t= 3x² i lufa — la – radius of convergence a) We know We know it ca)=1-2*0* Differentrating with (n=mtil {(11 nanas Inanal m { (-1) (meiam mso & Ez)" (m +1) ma For convergee 2t 12m + 2 min me lalu . Radims of convergence=4

4) We saw mao b (er eel" (m5) (21 (max) Put t=20 (-2), ** (mt) Multiply by a Ŝ 1920 for convergence losogat Lt 2 la1 m2 mti MyP eres lnlc | Radius of Convergence - ca