MATH 1XX3 Lecture Notes - Lecture 17: Dhow
12 Feb 2016
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Suppose you know ibn for all bn : an if. Andiverges , then so does bn if an converges then so does , bn. Notice that for all n , n2en" +1 (cid:15482) Since nt converges ( because it"s a p - series with p=2 the theorem says 1 also converges. "- as + tan and tn= bitbat . Since aiebi for (cid:15482) snetn for all n. Something you know ie geometric or a p - series. Example : decide if { sink ) convergeddiverges i in tq. Since lt let"s compare to "t = looks like so ettie ee dj ie feke with r= y. Thiscqnverges , anything about but you can"t conclude the 2nd series. Suppose an and bn with an , bn always positive. Then either both sequences converge or both sequences diverge. Example : an = , bn = ztn nhsmo n= ss = him. Converges , then so does i by limit comparison.
