Question

00 (1 point) For what values of 3 does the series (-1)"(5x)" converge? (n+8)(n +9) The series converges when is in Use interval notation to enter your answer. If the series converges at only one number, enter a closed interval or a single point, e.g., "[5,5]" or {5} Otherwise, enter an open interval (don't worry about whether the series converges at endpoints)

Answer 1

Ansi M8 5x).(ا) و بها ) (18) het an=(-15. (50)" ، رو + (48) ا+ ا+ا antl (1) .( 5 ) - Then Ratio test: len antl 71 an =) lim K-15+ (50) الما (۲۰۱۰) (و+ا) ناکا ( و ) ( 8 + ما) 5x) 1- (د) رود | رو در را که برد 6 راس را بندا ہے ارو)) (دا+ ما) ای به 1 و افراد نمیا و او را ره و رها 5 { * دواء lein (58) * - 8 زد 2 1 (6) team ادا 5 8 + ط (1+% 21 ) ار و سد لا دا +1) 71 |دا ( 74 < > < 5 5 NO: (\| A - XA

Now we will create the interminal of Conver -Convergence at and bont i-e at > and at na 5 arel Śj but na 1 in (-13h (-8)" { (-1) 2n 5 (-1) (n+8)(n+9) (n+8)(n+9) M8 r=0 (n+8) (nto) lin into K700 11 org # اص hty) 16h to) tante- Change het hy Converges at x = -1 8 li kowo ) 3-0 = li - 8 (finite no so the series Con 5

z no 11 hao 2 • but to = 1/3 in 15" (5434 *Eve (n+8)(h+9) (n+8) (h+9) (-1)" here an=fensa I (n+8)(n+o) (n+8) (uta) the t'ins=d ((n + 2)(n+997') (n+8)(n+8)) ya (n6)Cu+ y)) fin) = (n+8)+ (n +9).1 ((n + B)(n)) ((+8)(n+9))? So fon) is decrea sug fo .. Leibniz senės test: for = (2n+17) Lo for nzo 2 so using * 2-15 ano, Here nzo dn = bi antik an =) for all ("+9) Intro) (h+B)(n+g, and in 0; no(n+8)(249) Converges at 5) so o breall series (15(5%)" Converges in so the series at x= زا não (mts) (h+9) IA { 5 5 = HEL