Question

(2x-11)" 8) For the power series n? values it converges conditionally determine for what x-values it converges absolutely and for what x-

Answer 1

hiven senin 8 (2x-11) ہ nl e comparing with E an. at an= (x-1) nel (2x-11) antl = (2 n-11) (2x - 1) (n+12 n Cloth ) 2n-u aufl - and ant) 2x-ll an 2u-l anti em nia an nto 12x-ul Ito anal am no divergen, Rutio tert = 124-1) ahen lin-lil/216 the series is By 124-111=1 & absolutely anverges when 124-llal, ie -1 crunch alth <2u<ltll test taily to Lan C 12 Nent to cleak the 5 cncb fraz 5, 6 { (25)-11) converge we have Sergs [ Go. when n-S, we have nal n21 abso n2 p-seres test. converges lentely by alternating

when n=b serp (8 (0) -u)” (2-11), we have AM nas nr nal n n is also convergy abso solutely by ih i.e P-series teeb series is convergy absolutely for a, 55026 at [ 5,6 intravel I= [5,6 intravel of absolutely converges by 1 = [5, 6] conditionally converges : the There is na points for