Limited time offer 20% OFF StudySoup Subscription details

# UCR - MATH 009C - Calc 9C Week 4 Lecture Notes - Class Notes

### Created by: Layton Chhour Elite Notetaker

> > > > UCR - MATH 009C - Calc 9C Week 4 Lecture Notes - Class Notes

UCR - MATH 009C - Calc 9C Week 4 Lecture Notes - Class Notes

##### Description: Cover telescoping series, direct comparison test, limit comparison test, and ratio test to determine if a series converges or diverges.
Join more than 18,000+ college students at University of California Riverside who use StudySoup to get ahead
3 Pages 35 Views 28 Unlocks
• Notes, Study Guides, Flashcards + More!
Join more than 18,000+ college students at University of California Riverside who use StudySoup to get ahead
##### Description: Cover telescoping series, direct comparison test, limit comparison test, and ratio test to determine if a series converges or diverges.
3 Pages 35 Views 28 Unlocks
• Notes, Study Guides, Flashcards + More!

Unformatted text preview: Theorem 8.2.5 Changing finitely many terms in a series doesn't change whether it converges or not. Adding or removing fnitely many terms also doesn't affect convergence 23 converges it b only be converges if aisbi whenever in for some N. ab 1413 aj 1, 3, 5, 4, ,... bi 5, 7,100, 4, 5,... -) Sa come it 8 on le 3 a converges Telescoping Series What's tako s tot Does thus converte? Yes, because it's a long e os itin) Know converges by p-test (271). by Shrect comparison Lue Converges to it's even smaller! But what does it equa? ton ot - i.t-1 is to \$ : 34 35-*- \$ +... I 50 it's + + ++ crucial that semes comerye suce Mi+ 11. ero , beraue dontTheorem 16 lima other i contenes equals done L" Proof : Partial Sums are So. 20-21 20-3, S, do -3, +3, -az - 20 - az 2, 13, +1 -3 taz-az 2-ag ------- So l im S 0 slim 20-an - do S 20-30 Shce um ano (20-269)+(2+- 2) =(22-7"): (23-24)+(24_35) (-) + V-) + %-) V-**- \$)+.. 23-34 commerges 80 4 20 Here 3:52 mai sont conergos 35 . 2*-2-(*) Converges to. di 21:27 Theorem 8.3.2 Direct Comparison TSM If 04 Orson for an n then: 3 bn converges then an Comeryes ero te hype then o, but for larger's, nisbiy De bigger than the other m quatent: 1 2 an herges then in dverges if she come anything emailer wigs no Thanks to is a tt le sten n200, . in greuges -hts the hamaic sozs so pralary and in changes too. But notice s > Shce 12 n-In) > So Duted compaslar Test Soaps smce o fi deyes, entre diversos tooElampeestat You know & diverges net ,goonetik senes, and converges since 1111 21 geater than Notice C C 12" 22" (1262 m om deronter) te Drect Comparison Tests on canvas: betave Examples Meaning of more s athen an This is Problem similar to . 50 we guess .so we guess that that e con diverges, like hamericanes www sn, but comparison Test Songs of them drenges. we don't know she male is smaller than t. These 8.3.3 if in bn me Limit Componen Test sens & lin on Leat of 1 m Converges then sa Canverges. or f equivalently a n dierge 2 then bin dherges. on Use the Lime Comparison Test to carpe it so bok at T lo ime now- im + m 1 in) de by & burn u tom apades o age no way bigger than sont congue Test say dverges She did - limit 0, toe, Be be cadet if you top ons on and get &

×

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
We're here to help