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# Annotation of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.2_Summing_an_Infinite_Series/10.2.3.pg

 1 : aubreyja 2584 ## DBsubject('Calculus') 2 : ## DBchapter('Limits and Derivatives') 3 : ## DBsection('Definition of the Derivative') 4 : ## KEYWORDS('calculus', 'derivatives', 'slope') 5 : ## TitleText1('Calculus: Early Transcendentals') 6 : ## EditionText1('2') 7 : ## AuthorText1('Rogawski') 8 : ## Section1('10.2') 9 : ## Problem1('3') 10 : ## Author('Keith Thompson') 11 : ## Institution('W.H.Freeman') 12 : 13 : DOCUMENT(); 14 : loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl"); 15 : loadMacros("Parser.pl"); 16 : loadMacros("freemanMacros.pl"); 17 : loadMacros("PGauxiliaryFunctions.pl"); 18 : loadMacros("PGgraphmacros.pl"); 19 : 20 : #$showPartialCorrectAnswers=1; 21 : #add variation, LAD 22 :$c = Real(random(2,9,1)); 23 : 24 : $ans1=$c*(5/4); 25 : $ans2=$c*205/144; 26 : $ans3=$c*5369/3600; 27 : Context()->texStrings; 28 : BEGIN_TEXT 29 : \{ beginproblem() \} 30 : \{ textbook_ref_exact("Rogawski ET 2e", "10.2","3") \} 31 : $PAR 32 : 33 : Compute the partial sums $$S_2,S_4$$, and $$S_6$$. 34 : $c+\frac{c}{2^2}+\frac{c}{3^2}+\frac{c}{4^2}+\cdots$ 35 : 36 : 37 :$PAR $$S_2$$ = \{ans_rule()\} 38 : $PAR $$S_4$$ = \{ans_rule()\} 39 :$PAR $$S_6$$ = \{ans_rule()\} 40 : END_TEXT 41 : 42 : Context()->normalStrings; 43 : 44 : ANS(Real($ans1)->cmp); 45 : ANS(Real($ans2)->cmp); 46 : ANS(Real($ans3)->cmp); 47 : 48 : Context()->texStrings; 49 : SOLUTION(EV3(<<'END_SOLUTION')); 50 :$PAR 51 : $SOL 52 : $$S_2=c+\frac{c}{2^2}=c\left( 1+\frac{1}{4}\right)=c\left(\frac{5}{4}\right)$$; 53 :$PAR 54 : $$S_4=c+\frac{c}{2^2}+\frac{c}{3^2}+\frac{c}{4^2}=c\left(\frac{205}{144}\right)$$; 55 : \$PAR 56 : $$S_6=c+\frac{c}{2^2}+\frac{c}{3^2}+\frac{c}{4^2}+\frac{c}{5^2}+\frac{c}{6^2}=c\left(\frac{5369}{3600}\right)$$. 57 : 58 : END_SOLUTION 59 : 60 : ENDDOCUMENT();