Question

Problem 4. (12 points) Suppose that converges when -5 and diverges when : -7. Determine whether the foliowing series converge or dverge. Answer "Converges" or "Diverges." ? ? . 3. § (-1)", 12" Note: You only have two attempts at this problem Note: You can earn partial credit on this problem

Answer 1

power series is covergerent in(-R,R) or at x=R,-R but it is divergent other than these points

மிய & diverges at a=7 Cnxn converges at a=-5 neo L2RÀOÀài =IR) on Tower series conuerges de fer certain values and these values are always less than or equal to Radius of converence of Powen series e. g Power series à cet for C-R, R) but need no Since, given series us convergent at x=-5 & 1-5/<R = 5ER - te ga Power series comune no Radius of convergence is distance from centre I pt. at which to nearest series diverses given series Ance is at divergent a=7 60 R <7 ih uch them here xal & given series is convergent ② is a co(a)n here x=9>R 8 gunst. Zustour of un so given radius us less than neg. Hence given series us conurgent divergent ☺ LOCAL) here x = -9 € (-R, R) tience given series is son divergent ④ Againen (12)" (-1)) is divergent.