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Ernst_Maple_3__2__Fall_2007

# Ernst_Maple_3__2__Fall_2007 - MATH-I02 MAPLE ASSIGNMENT#3 I...

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MATH-I02 MAPLE ASSIGNMENT #3 I. Determine if the following sequences are convergent or divergent. Find the limit. Plot the sequences. a. b. c. lnn a =--- n 2 n II. Consider the series, a. Determine, by hand, the sum of the series, s. \1.·1 b. Use MAPLE to find the following nth partial sums. i) n=5 ii) n=10 iii) n=20 iv) n=40 (Notice that as n is increased, the nth partial sum approaches S)

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n=100 n=500 n=1000 III. Consider the series; '" 3 ~ n(n+3) a. Determine, by hand S n' the nth partial sum. b. Determine, by hand, the sum S of the series. c. Use MAPLE to determine s = lim Sn (the sum of the fC->'" series ). d. Use MAPLE to determine the following nth partial sums. i) ii) iii)
a:=n~--- 5 (n + 1) [> disp: =seq ([n,a (n)],n=l .. 50) : n: =' n 1 ; n:=n plot([disp] ,style=point); 0.16-l(> o 0.12 0.08 o o 0.04 o o 10 [> limit (a (n) ,n=infini ty) ; The sequence converges to O. 20 o 30 40 50

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19.91117680 > q:=Sum(exp(n) / (Pi" (n-l» ,n=l .. 30); 361""<-\ s"~ 30 q:= L -.!.. n n=lJr [> evalf (q) ; I > ql:=Sum(exp(n)/(Pi"(n-l»,n=1 .. 500); 5"'0"-'< ,>vW'\ 500 11 ql:= ~ _e_ kJ (n-1) 11= I Jr [> evalf (ql) ; [> 20.17367314
'].':1., 0.. "" 2: (or >i l"-t::t ~ ) =7 :. ".9- , - r- ~ '" y0 s - I . -() 11: _'1 (../- -f"'I ~b ~ '-I , ~ (~I (!"!-;) 2- co L I-IT S ::'2(,1 oc~ 1 00 ::c'7 ~ ( ~ - ~) I I l. \ I I I N(t-I~3) ~ \ - Ct .. l. •. } - (; .. ~ - :; ... ,...}":l 5 S, 5~ c y." '1 I' I I . (; 2- 5 TJ ? N~o ) ""3> .-.\ B C \ + '- , \ - - - :: -- + - ,..I~: l!.~ 1-1(1..!+3} 1-.' ~1·3 1-\; \ \' - - I J - S'" '" S ll""' S " = L ' '" ( , , .2.- ) \ . .•. - ~ ,- - .•... 1-)00 !J -'>Q:.I l 3 ,...1+\ ~1rL- M"'S ( \I ,... ~ ~". )~ Eo iJ +/ ,.1-', .,.1";'") j - 0 ~,;) C> - \ \ S 1-1 : - I-I-~ Cl:l b

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,- l> Rob Hubbard Calc-l 02 Assignment #3 [Problem la a: > ( I' II (/ .= II -1 _ ....

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