View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.2_Summing_an_Infinite_Series/10.2.1.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('1')
   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 Context()->variables->add(n=>'Real');
   22 $power=random(2,4);
   23 $p2=$power ** 2;
   24 $p3=$power ** 3;
   25 $p4=$power ** 4;
   26 
   27 $ans=Formula("1/($power ** n)");
   28 Context()->texStrings;
   29 BEGIN_TEXT
   30 \{ beginproblem() \}
   31 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","1") \}
   32 $PAR
   33 
   34 Find a formula for the general term \(a_n\) (not the partial sum) of the infinite series (starting with \(a_1\)).
   35 \[\frac{1}{$power}+\frac{1}{$p2}+\frac{1}{$p3}+\frac{1}{$p4}+\cdots\]
   36 
   37 $PAR \(a_n\) =  \{ans_rule()\}
   38 END_TEXT
   39 
   40 Context()->normalStrings;
   41 
   42 ANS($ans->cmp);
   43 Context()->texStrings;
   44 SOLUTION(EV3(<<'END_SOLUTION'));
   45 $PAR
   46 $SOL
   47 The denominators are powers of $power, starting with the first power. Hence, the general term is \(a_n=\frac{1}{$power^n}\).
   48 END_SOLUTION
   49 
   50 ENDDOCUMENT();