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| 1 : | gage | 5 | ##KEYWORDS('Series' , 'Divergent', 'Convergent' ) |
| 2 : | ##DESCRIPTION | ||
| 3 : | ## Determine if a series is convergent and evaluate it | ||
| 4 : | ##ENDDESCRIPTION | ||
| 5 : | |||
| 6 : | ## Shotwell cleaned | ||
| 7 : | |||
| 8 : | |||
| 9 : | ## DBsubject('Calculus') | ||
| 10 : | ## DBchapter('Infinite Sequences and Series') | ||
| 11 : | ## DBsection('Series') | ||
| 12 : | ## Date('6/3/2002') | ||
| 13 : | ## Author('') | ||
| 14 : | ## Institution('') | ||
| 15 : | ## TitleText1('Calculus Early Transcendentals') | ||
| 16 : | ## EditionText1('4') | ||
| 17 : | ## AuthorText1('Stewart') | ||
| 18 : | ## Section1('11.2') | ||
| 19 : | ## Problem1('23') | ||
| 20 : | |||
| 21 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 22 : | |||
| 23 : | loadMacros( | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGanswermacros.pl", | ||
| 26 : | "PGauxiliaryFunctions.pl" | ||
| 27 : | ); | ||
| 28 : | |||
| 29 : | TEXT(beginproblem()); | ||
| 30 : | $showPartialCorrectAnswers = 1; | ||
| 31 : | |||
| 32 : | $a = random(1,19,1); | ||
| 33 : | |||
| 34 : | BEGIN_TEXT | ||
| 35 : | Determine whether the series is convergent or divergent. If convergent, find the sum; | ||
| 36 : | if divergent, enter $BITALIC div $EITALIC. | ||
| 37 : | \[ \sum_{n=1}^\infty \frac{$a}{n(n+2)} \] | ||
| 38 : | Answer: \{ans_rule(20)\} | ||
| 39 : | END_TEXT | ||
| 40 : | |||
| 41 : | |||
| 42 : | ANS(num_cmp("$a*3/4", strings=>['div'])); | ||
| 43 : | |||
| 44 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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