## 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();