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UCR - MATH 009C - Week 2 Lecture Notes - Class Notes

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UCR - MATH 009C - Week 2 Lecture Notes - Class Notes

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School: University of California Riverside
Department: Applied Mathematics
Course: First Year Calculus
Professor: Steven Gindi
Term: Spring 2019
Tags: sequence, Series, and geometricseries
Name: Week 2 Lecture Notes
Description: Covered sequences and geometric series.
Uploaded: 04/15/2019
3 Pages 26 Views 20 Unlocks
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Unformatted text preview: When does a sequence "Converge? Rough definition we say a sequence an converges to some number L (the limit) if we can make an as close as we like to L by choosing n large enough (making a bigger and bigger) on when this happens Example 1) an has , , , ,... n2 13 14 This sequence comes to 20. We welimano Example has sino, sin 1, sin 2., sin 3,... 2) Does this converge : bn = sin(n) This does not converge SPUR say this s diverges & lima once is undefined Triangle Numbers 1+ 2+ 3+ + n(n+1 sum: nomine Product of 1-1-2-3..non! Convergence of sequences Definition: we say 3 sequence in converges to L if for any number E >O there exists 3 number N such that estion represent a ry name if n2N then lan- <E f you for ut enoun the distance better on in the ce n ter than when this happens we say an converges to L a n +00 or liman EL in converges. If an If an converges to some number 1, we say doesn't converge, we say it diverges.Example: Does On - converge? Yes, 16 dae E to, war N will mare if n then -o) < Ni will work since if nzn then t-o)-1)=*= to H E -100, N=102. w work (N-101 also works, we don't care 2102 then cho v what the sales it can be) For any 70, N +I will work : if n2N, then n2 +1, 50 Rules for Limits : Addition: if an & bn lim an + bn . - are Tim 0 two sequences , then an + w on if an bh converge Subtraction. In ano -- +60 man - +60 b it inton Converse + Multiplication Iim it in ann 1-400 limon -400 bn to be converge Division: lim o lim 2n if on 8 bn converge and lim Into 1-400 S get really small Example: lim +48 5+2n 6+ 6 it seems since when gets & tary by 5+ Or following the ries: Tim St walls of these its exist I 5+ lim5 m 2 5 + 2. limb + lim Vilim in po aus et se you Shale get a les in the endExample: im 4n+ 3 5n+ h But non doccige in hot keep getting lim 5nt So try something else: So this it n5+ m2 200 un sn Discussion 04110119 Converge or Diverge? + Ces (8+2) 00+ 8 + 220 1) 8 DE me then no converge og feier bh n 00 Emaer diverse (0-0) - inde l e C 2on2 - Jon - Concreto 2010 converget er r e diverse to co In(n), snak Small medium big polynomia: na exponential : ph Ki PER how fast they se approaching oo bigger bigger biggest

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