Question

Question 1. (a) Determine whether the series diverges or converges: Enal In (b) Determine whether the series 2n=1(-1)" 5 is absolutely convergent, conditionally convergent or divergent.

Answer 1

n Solution : Seneste long fan nth lern t२ or . E lnn nitn. . Taking the entegodt Since I nt. ln. n a n3+n+2 .. t. s Inn ntnt2 1+ 2 este II T2 (le ) ;.121 - . Taking ratio test, ie li ntx n'inta ngco 'in +1) +n +1 +2 n Scanned with CamScanner

nt n n +2 - ho 1+0+0) 2 1 e KOHT ) x (1+3) , 1x4 70 +0) *60*2)+53): 1 for I q ln(n) = By direct comparaison, ith term tert, So, (lacas)' = 47, Chitary's 3n+2 lin (In (n))' nosco antzy an anth ² nyo n (3% + 1) 1. Then a lim 1²v ht hoo to us Hence I + II E Inchi tn 1 to - 3+n+2 - 2 hence converges to @ Also, to (o s na Stran 1. Now this is Alternating revies, we are the Leibniz teit so nts ☺ so anti = (1+1²+5 . (2n+-3)2 ? , anzinets (2n-5)? so, ante > an uum wa no h→0 ห % zlem (1+) Hence it is So it Scanned with CamScanner 2. 1 to neither too convergent / conditionally or absolutely) is divergent . . .