(g) 1 2 3 P L K LLL Find the radius of convergence of the following power series: (a) 2 (d) 3kk 4k+5k (g) kk 1+2kkkk (b) * (e) (c) k22* (f) k=1 IMBIMBI k= 2k-2k k2+k (h) 2k 4kkk (i) k=1 IM8M81 (log k)/2k k=3 k!z k=1 We apply the ratio test, thus kk R = lim = lim k-00 ak+1 k-001+2kkk k 1/k = lim kk = lim 1+2+1 (k+1)+1 k (k+1) (1+2kkk) (k+1) 1+2+1 (k+1)+1| (k+1)+1 1 (1+2kk) (k+1) 2k+1 (k+1) k- 1+1/k + 1+2kk k 1/k k 1 k+1 1 == lim k-x 1+1/k +2 = 2. (1+2kkk) (k+1) k 1/(2kkk) + (h) We apply the root test, thus 24