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# Class Note for MATH 1432 at UH

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This 116 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15

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3 my 2 Z 5k mag 34 V i Zgwwem 234 z mmg mfz n H dews f1rae 2 aazg u 2 mg k Emma y an k 2 ng u 5 m N m k M M E 2k 1k e Azg ZWWMSH 2 a r 2 377 mm in 522 EN gaawmga a 3 m u mi 4 A SW 2 u 5 u w mnvagezhm uiekl w M auxmg pk mmg menzakmwg I w M mnVHSS wequot 2 wags e 25mm mnvagent sen m Convergent 9mmquot mam Aseugzakwuwm MW w M mg 1 e 25mm mnvagent sen m Convergent 39 um Nana mm P x A 2 1 2 p gt L mwg MW we 2 wag pk mmg menzakmwg I F W 154 m 4 x v 34va 4 lt x lt L mmmmw house 2 x mng 9mmquot mam Aseugzakwuwm MW w M mg 1 e 25mm mnvagent sen m Convergent 39 um Nana mm P x A pk mmg menzakmwg I ii 27 2 32 F W 154 m 4 u r 34va 4 lt x lt L mmmmw house 2 x mng e mme mm 7 mm mm 2 21 27 21 1e y N 33 z mam M m 3 5 5333233 A M 322mm 2 ME 22W 3 Y A SW ak 5 u w mnvagmmmw w Zak auxmg We 2M tinmg WW 0 A SW ak 5 u w mnvagmmmw w Zak auxmg We 2M tinmg WW 0 m m be gamma powE numbers m m be mm W mm 2W imam 5 Guy in z mmwg m m be mm W mm 2W imam 5 Guy in z mmwg m m be damsmg quenm m pomE numbas m m be mm W mm 2W imam 5 Guy in z mmwg m m be damsmg quenm m pomE numbas mm M Ewywwg LMFWWEL39K 12 m m be mm mm mm 2w imam 5 Guy in z mmwg awquot harm m m be dmsmmuenm m mm mm Mu M ZHVWWg wagarm H 282 qDwi r n PgtU zumampv 5me WWW 23 m m be aimed pm mm Dam hawking 5 Qua in 2mmqu lama berm m m be dmsmmuenm m mm mm Mu M ZHVWWg ymym r qubwi r f n 21 35 PgtELzomIEV 5vre 39x g sdmsmg 3 m ngpwmu imm 7 k 5 mmgezwmmuy WWW 23 m m be aimed pm mm Dam hawking 5 Qua in 2mmqu lama berm m m be dmsmmuenm m mm mm Mu M ZHVWWg ymym r qubwi r f n 21 35 PgtELzomIEV 5vre 39x z sdwsmg 3 quota ixfiygt quxgtElgndxlmwlbdz Eur J k 5 mmgezwmmuy 2k1 4V 2 mwgem m zm mwgm Z quot5 mmgem 2k1 2x1 Edaeasms e M L E x 02gt fquxgtEL m x ZW WWWWzm smsmm 39 quotXZWgtmm xgt ru Z quot5 mmgem 2k1 2x1 mm M NH Azim 4 w x z mwgm 39x zm mmsmg m z W gtu nmm gym u m w Alternating Series An Estimate for Alternating Series l lllllll l 0 S1 S3 S5 L S4 S2 S0 An Estimate for Alternating Series Jiwen He University of Houston Math 1432 Section 26626 Lecture 24 April 10 2008 quot 1 an gar2 Alternating Series An Estimate for Alternating Series lllllllll L S4 S2 S0 0 S1 S3 S5 An Estimate for Alternating Series Let ak be a decreasing sequence of positive numbers that tends to O and let L Z 1kak kO April 10 200839 Math 1432 Section 26626 Lecture 24 Jiwen He University of Houston quot 1 an gar2 Alternating Series An Estimate for Alternating Series l lllllll l 0 S1 S3 S5 L S4 S2 S0 An Estimate for Alternating Series Let ak be a decreasing sequence of positive numbers that tends to O and let L Z 1kak Then the sum L lies between kO consecutive partial sums 5n sn1 sn lt L lt sn1 if n is odd sn1 lt L lt 5 if n is even Jiwen He University of Houston Math 1432 Section 26626 Lecture 24 April 10 200839 quot 1 an gar2 Alternating Series An Estimate for Alternating Series l lllllll l 0 S1 S3 S5 L S4 S2 S0 An Estimate for Alternating Series Let ak be a decreasing sequence of positive numbers that tends to O and let L Z 1kak Then the sum L lies between kO consecutive partial sums 5n sn1 sn lt L lt sn1 if n is odd sn1 lt L lt 5 if n is even and thus sn approximates L to within an1 lL snl lt an1 Jiwen He University of Houston Math 1432 Section 26626 Lecture 24 April 10 200839 rm WWW mmquot m4 0m w 7 72 rm s m zpwmu EAT g mmquot m i L iii y 7 72mm 5314 k k FuL Akm z mmquot m2 rm WWW g W 2 gk rm mnmu mew Er e n2gt102 e quotgt98 mmquot m2 rm WWW g k1 a 0 W nkmamm t 2 man e n2gt102 e quotgt98 99m 09 gm vimz sum lm 5 stm2 3 E mu mmquot m2 rm WWW g k1 a 0 W nkmamm t 2 man e n2gt102 e quotgt98 99m 09 gm vimz sum lm 5 7 Eu5m2 rmmuemmu er ltzm m91 mmquot m2 rm WWW g k1 a 0 W nkmamm t 2 man e n2gt102 e quotgt98 99m 09 gm vimz sum lm 5 7 Eu5m2 rmmuemmu er ltzm m91 we zondude m swusemzigmzmummmm H Sn memig m2 Wm ll Sn mwmwig m2 Wm pm 734 lt ma Wm ll Sn mwmwig m2 Wm pm 734 lt ma Wm 39MquotWlt quot quot3 ll Sn memig m2 Wm pm 734 lt ma Wm 39M 20 1 1 mama panama s 175NDBZZZ ch e quot2 mquot ll Sn memig m2 Wm pm 734 lt ma Wm 39M 20 1 1 mama 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