View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.9.pg

    1 ## DBsubject('Calculus')
    2 ## DBchapter('Infinite Sequences and Series')
    3 ## DBsection('Infinite Sequences and Series')
    4 ## KEYWORDS('calculus', 'series')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('10.1')
    9 ## Problem1('9')
   10 ## Author('LA Danielson')
   11 ## Institution('The College of Idaho')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 Context()->texStrings;
   19 
   20 sub harmonic_sum {
   21     $n = shift;
   22     $sum = 0;
   23 
   24     for($i=1; $i<=$n; $i++){
   25       $sum += 1/$i;
   26     }
   27 
   28 #    $ret_val = $sum;
   29 
   30     return $sum;
   31 }
   32 
   33 $a = Real(random(2,9,1));
   34 
   35 $c1=$a*harmonic_sum(1);
   36 $c2=$a*harmonic_sum(2);
   37 $c3=$a*harmonic_sum(3);
   38 $c4=$a*harmonic_sum(4);
   39 
   40 BEGIN_TEXT
   41 \{ beginproblem() \}
   42 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","9") \}
   43 $PAR
   44 Calculate the first four terms of the following sequence, starting with \(n=1\).
   45 
   46 \[c_n=$a+\frac{$a}{2}+\frac{$a}{3}+\ldots+\frac{$a}{n}\]
   47 
   48 \( c_1 = \) \{ans_rule()\}$BR
   49 \( c_2 = \) \{ans_rule()\}$BR
   50 \( c_3 = \) \{ans_rule()\}$BR
   51 \( c_4 = \) \{ans_rule()\}$BR
   52 END_TEXT
   53 Context()->normalStrings;
   54 
   55 ANS($c1->cmp);
   56 ANS($c2->cmp);
   57 ANS($c3->cmp);
   58 ANS($c4->cmp);
   59 
   60 Context()->texStrings;
   61 SOLUTION(EV3(<<'END_SOLUTION'));
   62 $PAR
   63 $SOL
   64 Setting \(n=1,2,3,4\) in the formula for \(c_n\) gives $BR
   65 \(c1=$c1\)$BR
   66 \(c2=$a+\frac{$a}{2}=$a\left(\frac{3}{2}\right)=$c2\)$BR
   67 \(c3=$a+\frac{$a}{2}+\frac{$a}{3}= $a\left( \frac{11}{6}\right)=$c3\)$BR
   68 \(c4=$a+\frac{$a}{2}+\frac{$a}{3}+\frac{$a}{4}=$a\left( \frac{25}{12}\right) = $c4\)
   69 END_SOLUTION
   70 
   71 ENDDOCUMENT();