math1B-Spring_2006-mt2-Ratner-exam

math1B-Spring_2006-mt2-Ratner-exam - 1(20 points Does the...

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Unformatted text preview: 1. (20 points) Does the following sequence {an} converge? If yes, find its limit. Justify your answers. a) (10 points) \0 “"=(2+(1—1)n)n 3.09,, 6004 )g 4,. "’ _ Hm (JT M 5 ,L__ ‘4 W: (2" - W’sb 1 J ‘ (3 ) H) : I Z O 2 Sin/b Santa Wfil’fi flmfié 50 4 3 l ‘ ’ ’M. b) (10 points) 3 \9 0‘" = (7+(—1)")n W . In .12, (£7) = (5.)” Test the following series for convergence. Justify your answers. 2, (10 points? 0'“ 00 '~ 1 __|_ / sm— ‘ , Z «in m'é‘mh‘ Wéw I la‘ [9,, = 13/17 71:1 I "7” h \ 5'” i; ’ M 3/1 H Um 51.01 ‘Hlbh n¢>¢a b,’ ‘ Um ‘ ‘4‘)” VJ; ' )0sz NM!" Silk D] / 4. (10 points) jw —> 0”” 40“?" a , . I XL #14:; v::L k4: _: -2Msc I no xi /' HM ~2In+ q Zlm 7W» 7? ‘ +*1 7‘ t ’ 7' a}? fig! ‘\\) L” L f-F J “m _"',, “MW . _ +-:~eo ~17; '3 I”: A MWM A 60 E 'Zlmx xi +fo 70 L! 4 J. ,i E. 2 2L; g 5. (10 points) 6. (10 points) 00 —1 n ‘ 7. (20 points) Consider Z ( ) In R. TL n=1 3.) (10 points) Does the series converge? b) (10 points) Does the series converge absolutely? Justify your answers, b”: $00): :uwmsréh ,wc'oohfl’kj'w ’ k F/(X): I‘X/fx t) W yaw 0/ @318 (B M amf/W. ./ 4 50 M Mr Du :1 g/yfigflw g: i J o F g: : o , W A A:\ \ 3” ® 9W «.1 gm: rs Show *a A4 W47 WWW, MM’MMW. 0 ...
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math1B-Spring_2006-mt2-Ratner-exam - 1(20 points Does the...

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