midterm1 - V ru-(-{ ~rflh ()t-7 d2J ~. ~'rm fA-70() Answer...

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- - / , .1 Name ~ 15 Math 253 Midterm 1 (100 points) 1. Determine weather the sequence converges or diverges. If it converges, find I ~ the limit: 10 n2 sin(n) a = 11 n4 +2 o~ / . rn2J;'77(/f» ) - (fIV ,J- .Q - m2 ) h'nfl7) I 111+02 InL <- - ').0 - ?1 ~-f-. .2 N -? ()(] Answer 4?r'Uf=O, ~u~7Iz~ ~ . . 2. Delermine weather the series is convergent or divergent. If it is convergent, find its sum: 02() aJ f1~:" := Z (- . It' 1- 11- ) rn -=- -b . J -r 2- D.!-.-::: 11=1 (>7::-1 ~ 5 ( 5 tJ I -~ b I -- ~ = !- + 3 -(7\ LI ~ - '\5.) , Answer
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---- b) f 3 (Telescopic series) n=! n(n + 3) - 1 ) := (! - -0 + (L . - . . -- . \ . ) 1- ( 1 . ~ ~' ) t M,f- 3' ~ / 2 £) B b I .+1-. .i- J- := 2 g lr~ f/1-=- / - C:, Answer 3. Determine whether the series is convergent or divergent: -15' f 2(-1)" + sin(n) n=! n 2 + 3 DO +- Z ~'m(?) 11~1 1A ~-t3 ()b 1 :2 (-I) 'Y) '11/1 f/1 2.-+ 3 - Cff7t I/~ euJ- a bJ C;SY) v ( UWf -!€A) lli J C51\V O;-nV ( Mi. jVLIeJ M ) Answer
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-- - . 4. Determine whether the series is absolutely convergent: to : f (-9)" 11=0 n! I ' (-Cf )'14.+1 'Yl '. \ ~-(-i)1 . C-q)1h = 1 - q \ = 0 <::: 1 -) A bS, 0m
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Unformatted text preview: V ru-(-{ ~rflh ()t-7 d2J ~. ~'rm fA-70() Answer Ii~ CmtVk~ 5. Find the radius of convergenceand interval of convergenceof the series: ~J5 f (X-2)1I 11=1 n 2 + 1 'ttL+ \ I . eX -2)?J (= (9)-1 ~X-,2 <: \ 1 C::Xc.3 ) 0~)?h-) Q:t,t-' )1--+ (-J x-..21 < I (7.J 00 AnswerR == I 2 7: ==-[ I.) 3J x, '-=> Z C-t)0) CAI1v (M:t ) 1'1\L+) X 3-=> Z-1-U\>I. if ( 1-& . I'lli:" ) 1{ 'I , 6. Use series to evaluate the limit: If) I " sin(x) -x 1m X~O x3 d/rn(j<) ~X [ y-~ +~-2- -V(jl . +-- . X20-.. ,1 )(3 ,XS"" >< z,--+-_x t E)f-,--t--~o 7! X3 ]-><- ---~. +x 1-y 3' ~-~-I-" 51 I ! X ~(fJ v-Answer I-'~~-(0-~ 7. Find the sum of the series: 10 ~ 2n 2:-n=O3n n! 00 2 c~ j'YJ r77 =0 fill-G) Answer ;:?;)...
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This note was uploaded on 08/17/2009 for the course MATH 253 taught by Professor Poplicher during the Spring '08 term at University of Cincinnati.

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midterm1 - V ru-(-{ ~rflh ()t-7 d2J ~. ~'rm fA-70() Answer...

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