MATH 31B Lecture 23: Integral, Direct Comparison and Limit Comparison Test
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Nextup i:l: est (cid:8869) direct comparison test (cid:8869) limit comparison test. Recall given a series eagan , we let sn=n=e2an= a. start . Egan{= diff sn diverges , if that limit exists; otherwise . Them (sum laws) if ean r e bn converge , we get : laws then. Lant bn] = far + en brr. Rmi & combined give { can - bn] = en an - ibn. Motivation: many giver value it times all we need to figure out is whether a not necessarily the converges or diverges , series converges to (if it converges. Let f-cx) be a function which is positive, decreasing, this is. I m sat . i. e. and continuous for all large enough x true for all xzm . Egan converges,(cid:12200) faadx converges (any starting place ) ( if and only if " ) Ciel, test, f- cx> = it is postie , decreasing ,
