Question

Which is series divergent? ο Σ=1 1,000,000+η 1 1 Σ=1 1.2 1 Σ En=l n2 Σ=1 an+1

Answer 1

a poseeles test 2 hp nel Þ31 ate both positive Connages if þ>t and diverges it limit comparision test let Ean and Ebn term series such that Ean is unknown and Ebn is known series it limca on 70,00 both Ean, Ebu "Converges used as diverges together u Ean- Ë 1000000th and Ebn=8 non zero finite then n=1 hel Now lim an hyco bn lim 1000000 un lim ho h 1000000+h h-as = lim an bn = lim h) to hyeo 1000000 +1 100000 to 1000000 n neco - lim an # 0,00 ισοσοσο ie non zero finite bn hence Zan and Ebn both converges or diverges together but Ebn = Et is diverges (by p seles test hence Ean รี is divergent : P-1 00 1000000th h=1 00 converges po p=1,2 > 1 no 2 (a) Ë (ii) . nel is converges P = 2 > 1 10 hel (iv) let Şana and Ebn=En3/2 U M18 n (Jnts) h=1

an n/ n3/2 then lim N-00 bn hyoo nunti h-no 1312 lim an h-oo bn lim h-oo -1 1 q lim an i.e non zeeo finite lim mir () with 2 +0,00 h100 bn hence Ean and Ebn both but {bn = { 13 & hole is converges by posesies test :: P = 3 >1 hence {an= E nunta) conveges together is converges h=1 hence only siwi is diverges 1000000 th hal
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