## DBsubject('Calculus')
## DBchapter('Limits and Derivatives')
## DBsection('Definition of the Derivative')
## KEYWORDS('calculus', 'derivatives', 'slope')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('2')
## AuthorText1('Rogawski')
## Section1('10.2')
## Problem1('1')
## Author('Keith Thompson')
## Institution('W.H.Freeman')

DOCUMENT();
loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
loadMacros("Parser.pl");
loadMacros("freemanMacros.pl");
loadMacros("PGauxiliaryFunctions.pl");
loadMacros("PGgraphmacros.pl");

#$showPartialCorrectAnswers=1;
Context()->variables->add(n=>'Real');
$power=random(2,4);
$p2=$power ** 2;
$p3=$power ** 3;
$p4=$power ** 4;

$ans=Formula("1/($power ** n)");
Context()->texStrings;
BEGIN_TEXT
\{ beginproblem() \}
\{ textbook_ref_exact("Rogawski ET 2e", "10.2","1") \}
$PAR

Find a formula for the general term \(a_n\) (not the partial sum) of the infinite series (starting with \(a_1\)).
\[\frac{1}{$power}+\frac{1}{$p2}+\frac{1}{$p3}+\frac{1}{$p4}+\cdots\]

$PAR \(a_n\) =  \{ans_rule()\} 
END_TEXT

Context()->normalStrings;

ANS($ans->cmp);
Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
$PAR
$SOL
The denominators are powers of $power, starting with the first power. Hence, the general term is \(a_n=\frac{1}{$power^n}\).
END_SOLUTION

ENDDOCUMENT();