Notapower series defined because center yes power series centered at 0 Not a power series powers the first terms are negative Not an a power integer series because exponent is not yes its a power series centered at 5 No its not because exponent is negative Lim n x 3 3 21 x 3 22 G2n 1 n X Radius 2 S S Lim X S 2n 2 2n 1 2n n x n D A S Radius O for X 0 S Lim n x Cucunty S 14 1 x Radius 2 Lim n X 1 2n 3 X K nt 1 2n 3 un 2 0 radius by ratio test 1 L Liny 1 n3 S n D x 2 n 1 x 212 9 1 x 2 13 Radius 3 MATH 141 Homework 12 3 Suppose that the power series cn x 2 n converges for x 6 and diverges for x 6 What must be true about the radius of convergence R R 1Xn 0 divers I b C I 4 converses Converge I I diverse I 2 8 6 R 4 x 2