#DESCRIPTION
##  Calculus: Absolute convergence and the ratio and root tests
##ENDDESCRIPTION

##KEYWORDS('calculus', 'series', 'ratio test')

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Absolute Convergence and the Ratio and Root Tests')
## Date('04/07/2010')
## Author('Justin Sukiennik')
## Institution('University of Minnesota')
## TitleText1('Calculus: Concepts and Contexts')
## EditionText1('4 Custom UMTYMP Ed.')
## AuthorText1('Stewart')
## Section1('11.6')
## Problem1('1')

#####################################################################
DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "PGunion.pl",
  "parserPopUp.pl",
  "PGchoicemacros.pl",
  "PGcourse.pl", 
);

#####################################################################
install_problem_grader(~~&std_problem_grader);

TEXT(beginproblem());

$showPartialCorrectAnswers = 0;

#####################################################################


Context("Numeric");

$a = list_random(2,4,5,10,20);

$b = Compute("1/$a");

$popup1 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Convergent');
$popup2 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Inconclusive');
$popup3 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Divergent');

#####################################################################

#Title("$BITALIC Look Ahead: $EITALIC 11.6 Absolute Convergence and the Ratio and Root Tests");

Context()->texStrings;
BEGIN_TEXT
What can you say about the series \(\sum a_n\) in each of the following cases using the Ratio Test?  Answer "Convergent," "Divergent," or "Inconclusive."$BR
$HR
\{$popup1->menu\} $BBOLD 1. $EBOLD  \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = $b\) 
$PAR
\{$popup2->menu\} $BBOLD 2. $EBOLD  \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = 1\)
$PAR
\{$popup3->menu\} $BBOLD 3. $EBOLD   \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = $a\)
$HR
$BBOLD Note:$EBOLD  $BITALIC You only have two attempts at this problem.$EITALIC
$HR
END_TEXT

#####################################################################

ANS($popup1->cmp);
ANS($popup2->cmp);
ANS($popup3->cmp);

ENDDOCUMENT();        # This should be the last executable line in the problem.