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# View of /trunk/NationalProblemLibrary/Rochester/setSeries5IntegralTest/eva8_3_3.pg

Mon May 8 17:05:32 2006 UTC (7 years ago) by jjholt
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Added tags.


    1 ## DESCRIPTION
2 ##   Infinite Series with the Integral Test
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Series', 'Converge', 'Diverge', Integral Test')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Infinite Sequences and Series')
10 ## DBsection('The Integral Test and Estimates of Sums')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$a = random(2,9,1);
34 $b = random(2,8,1); 35$c = $a*$b-$a; 36$e = $a +$a -2;
37 $d = ($e)**($b-1) ; 38 BEGIN_TEXT 39 Find the value of 40 $\int_2^{\infty} \frac{dx}{(a x-2)^b}$$BR
41 \{ans_rule(20)\} $BR 42 Determine whether$BR
43 $\sum_{n=2}^\infty \frac{1}{(a n-2)^b}$ $BR 44 is a convergent series. Enter C if series is convergent, D if series is divergent. 45 \{ans_rule(1)\}$BR
46
47 END_TEXT
48
49 $ans1 = 1/($c*$d); 50$ans2 = "C" ;
51 ANS(num_cmp($ans1)); 52 ANS(str_cmp($ans2));
53
54 ENDDOCUMENT();        # This should be the last executable line in the problem.