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

    1 ## 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();