1 2 3 P LLL Find the radius of convergence of the following

Last updated: 5/22/2023

1 2 3 P LLL Find the radius of convergence of the following power series a b c k k 1 R lim LK We apply the ratio test thus ak 2 d k ak 1 e k k f lim IMBIMBIM8 k h We apply the root test thus 3k k 4k 5k ko 1 2kkk 1 2 1 k 1 k 1 k 1 k 1 lim 1 kx 1 1 k 1 2kkk k 1 2k 2k k k 4kkk kk ko k 1 k k 1 k 1 Jimm 1 1 6 1 2 5 1 1 1 2 1 1 k 2kkk k 1 kk g h i 24 log k 2k k 3 k 1 kk 1 2kkkzk lim 1 2 1 k 1 1 2kkk k 1 2k 1 k 1 1 2kkk