Question

DETAILS 1. [-/5 Points) MY NC Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) 1 + x Σ provided 1x1 no 2. [-/5 Points) DETAILS MYN Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) 5 f(x) 1 + Σ provided fx < no 3. [-15 Points] DETAILS MY Find a power series representation for the function; find the radius of convergence, R. (Give your power series representation centered at x = 0.) f(x) = ln(1 - 2x) Σ provided R = no

Please help solve all of them!

Answer 1

function find the interval ab. conuergence. Find a 0 power series representation for the f(x) = 9 9 tä solution Given that 9 fcx) 1+2 Now from Hee geometric sevier. 2 a 1812I & arm 01-0 Now we talce a: 9 ; r=-X L E mo6 (9) (-2) lalli Ex)" 1 : 1221 3 ) 9 € m20 o 5 f (2) - 14x² Solution Given thal ร f(x) 1722 How from the geometric series ol? a & aign. -7 no 5 1-(-2) 2 Iselli } @ 5.(+223"); Thank youu