View of /trunk/NationalProblemLibrary/Rochester/setSeries1Definitions/ur_sr_1_6.pg

    1 ## DESCRIPTION
    2 ##   Series Notation
    3 ## ENDDESCRIPTION
    4 
    5 ## Tagged by nhamblet
    6 
    7 ## DBsubject('Calculus')
    8 ## DBchapter('Infinite Sequences and Series')
    9 ## DBsection('Infinite Sequences and Series')
   10 ## Date('6/3/2002')
   11 ## TitleText1('Calculus: Early Transcendentals')
   12 ## AuthorText1('Stewart')
   13 ## EditionText1('6')
   14 ## Section1('11.1')
   15 ## Problem1('25')
   16 ## KEYWORDS('Series', 'Finite','')
   17 
   18 DOCUMENT();        # This should be the first executable line in the problem.
   19 
   20 loadMacros(
   21 "PG.pl",
   22 "PGbasicmacros.pl",
   23 "PGchoicemacros.pl",
   24 "PGanswermacros.pl",
   25 "PGgraphmacros.pl"
   26 );
   27 
   28 TEXT(beginproblem());
   29 $showPartialCorrectAnswers = 1;
   30 
   31 $a = random(3,5,1);
   32 $b = random(-5,10);
   33 $c = random(1,3,1);
   34 
   35 if ($a == 3) {$ans = $c**2 - ($c+1)**2 + ($c+2)**2 - ($c+3)**2 + 4*$b;}
   36 if ($a == 4) {$ans = $c**2 - ($c+1)**2 + ($c+2)**2 - ($c+3)**2 + ($c+4)**2 + 5*$b;}
   37 if ($a == 5) {$ans = $c**2 - ($c+1)**2 + ($c+2)**2 - ($c+3)**2 + ($c+4)**2 - ($c+5)**2 + 6*$b;}
   38 
   39 BEGIN_TEXT
   40 Evaluate the sum:
   41 \[ \sum_{k=0}^{$a}{((-1)^k (k+$c)^2+$b)} \]
   42 \{ans_rule(20)\}
   43 
   44 END_TEXT
   45 ANS(num_cmp($ans, mode=>"arith"));
   46 
   47 ENDDOCUMENT();       # This should be the last executable line in the problem.