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| 1 : | jjholt | 202 | ## DESCRIPTION |
| 2 : | ## Series Notation | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 141 | |
| 5 : | jjholt | 202 | ## Tagged by nhamblet |
| 6 : | |||
| 7 : | jj | 3115 | ## 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 : | jjholt | 202 | |
| 18 : | jj | 141 | 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. |
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