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| 1 : | gage | 5 | ##KEYWORDS('Sequences', 'Comparison Test') |
| 2 : | ##DESCRIPTION | ||
| 3 : | ## Determine if a series converges | ||
| 4 : | ##ENDDESCRIPTION | ||
| 5 : | |||
| 6 : | ## Shotwell cleaned | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Infinite Sequences and Series') | ||
| 10 : | ## DBsection('Alternating Series') | ||
| 11 : | ## Date('6/3/2002') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('') | ||
| 14 : | ## TitleText1('Calculus Early Transcendentals') | ||
| 15 : | ## EditionText1('4') | ||
| 16 : | ## AuthorText1('Stewart') | ||
| 17 : | ## Section1('11.5') | ||
| 18 : | ## Problem1('15') | ||
| 19 : | |||
| 20 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PGbasicmacros.pl", | ||
| 24 : | "PGanswermacros.pl", | ||
| 25 : | "PGauxiliaryFunctions.pl" | ||
| 26 : | ); | ||
| 27 : | |||
| 28 : | TEXT(beginproblem()); | ||
| 29 : | $showPartialCorrectAnswers = 1; | ||
| 30 : | |||
| 31 : | $a = random(1,4,1); | ||
| 32 : | $b = random(5,9,1); | ||
| 33 : | |||
| 34 : | BEGIN_TEXT | ||
| 35 : | Determine whether the following series converges or diverges. | ||
| 36 : | \[\sum_{n=1}^\infty\frac{ \cos(n\pi) }{ n^{$a/$b} }\] $BR | ||
| 37 : | Input $BITALIC C $EITALIC for convergence and $BITALIC D $EITALIC for divergence: \{ans_rule(1)\} | ||
| 38 : | $BR$BR $BBOLD Note: $EBOLD You have only one chance to enter your answer! | ||
| 39 : | END_TEXT | ||
| 40 : | |||
| 41 : | ANS(str_cmp("C") ); | ||
| 42 : | |||
| 43 : | ENDDOCUMENT(); # This should be the last executable line in the problem. | ||
| 44 : |
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