Question

1. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. a) (-3) * 2. (2n + 1)! b) (2n)! 2 (n! 2. Find the radius of convergence and the interval of convergence.

Answer 1

(-3) Elgh zh no (2 ha) (2na)! Let un 3 (2nd) Here unaik in v u un is monotonically decreasing This, by Leibnitz test 5 Elgh 3h is cong ondig, is converge 'Let an= (-33h (and)! Now, Slanlar (2nd)! Zlonias on shah 0 (2 ntg)! alim co (2nd) (2ndan 2 ha)! ah haya ok 2 jam) is convergent.. This s Eigh gh is absolutely an (2nA! convergent

(22) ! him and a lim & hae), (h! 2 ha un (ha)! Ond! Slim (2n+2) Candy (na 2 (26%) (2+ yeni - lim by D-alembert dess E en is divergond also this is not : absolutely converget. A 2) 22h, het R be R.O. and Lan » R = o.) je Then Roo.c of H 22h R=0 is R2 - (cos.co.

I i interval af ka convergence is – a La Loo ie & aco) (20-ih 6.3 comentat coxy". shath no b - lim 1 ans sinin Il lim n In stant en interval of convergence : z <R ( x LS 3 - CBX = -22223 (-2,3) coe will check = -2; 3 eit des 2 un Shah - light is coverage 2 2 at oshgn x = 3 an S - is divergent share a

i interval af convergence a [2,3)
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