##DESCRIPTION ## Simplifying factorials ##ENDDESCRIPTION ## KEYWORDS('Sequences and Series') ## Tagged by ynw2d ## DBsubject('Algebra') ## DBchapter('Sequences and Series') ## DBsection('Arithmetic Sequences') ## Date('') ## Author('') ## Institution('ASU') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') ##KEYWORDS('algebra', 'sequence') ##KEYWORDS('factorials') # # First comes some stuff that appears at the beginning of every problem # DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGasu.pl", "extraAnswerEvaluators.pl" ); TEXT(&beginproblem); # # Now we do the randomization of variables, and other computations # as needed for this problem. Sometimes we compute the answers here. # #pick the coefficient for n $a = random(2,4); #pick the number to add to the numerator$b = random(1,4); #pick the number to add to the denominator $c = random (1,3); #this will compute the answer to the problem #set the answer to the first possible term$ans = "($a*n-$c+1)"; #concatenate the rest of the terms up to $b for($j=-$c+2;$j<=$b;$j++){$ans.="*($a*n+$j)";} # # Now the problem text itself, with ans_rule's to indicate where the # answers go. You can stop entering text, do more computations, and then # start up again if you want. # BEGIN_TEXT Simplify the expression $\frac{(a n + b)!}{(a n - c)!}$.$PAR $$\frac{(a n + b)!}{(a n - c)!}$$= \{ans_rule(40)\} END_TEXT # # Tell WeBWork how to test if answers are right. These should come in the # same order as the answer blanks above. You tell WeBWork both the type of # "answer evaluator" to use, and the correct answer. # &ANS(fun_cmp(\$ans, var => 'n')); ENDDOCUMENT(); # This should be the last executable line in the problem.