{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–4. Sign up to view the full content.

- - / , .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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
---- 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
-- - . 4. Determine whether the series is absolutely convergent: to 12af>&- Ted : f (-9)" 11=0 n! I ' (-Cf )'14.+1 'Yl '. \ ~-(-i)1 . C-q)1h = 1 - q \ =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: V ru-(-{ ~rflh ()t-7 d2J ~. ~'rm fA-70() Answer Ii~ CmtV€k~ 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 ;:?;)...
View Full Document

{[ snackBarMessage ]}