View of /trunk/rochester_problib/setSeries4Geometric/ur_sr_4_1.pg

    1 #DESCRIPTION
    2 #Limits of sequences
    3 #ENDDESCRIPTION
    4 
    5 #Keywords('Series ' ,'Limits')
    6 
    7 DOCUMENT();
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl"
   14 );
   15 
   16 TEXT(&beginproblem);
   17 
   18 $showPartialCorrectAnswers = 0;
   19 $a=random(2,3);
   20 $b=random(4,10);
   21 $c=random(4,10);
   22 $d=$c+1;
   23 $e=random(3,9);
   24 
   25 $ans0="DIV";
   26 $ans1=(1/($a**2))/(1-(1/$a));
   27 $ans2=(1/$b)/(1-($a/($b**2)));
   28 $ans3=($c**5/$d**5)/(1-($c/$d));
   29 $ans5=($c/$d)/(1-($c/$d))+ ($a/$d)/(1-($a/$d));
   30 
   31 TEXT(EV3(<<'EOT'));
   32 
   33 The following series are geometric series.
   34 $BR Determine whether each series converges or not.
   35 $BR For the series which converge, enter the sum of the series.
   36 For the series which diverges enter "DIV" (without quotes).
   37 
   38 $BR (a)  \( \displaystyle \sum_{n=1}^{\infty} \frac{$d^n}{$c^n} = \) \{ans_rule(20)\},
   39 $BR (b)  \( \displaystyle \sum_{n=2}^{\infty} \frac{1}{$a^n} = \) \{ans_rule(20)\},
   40 $BR (c)  \( \displaystyle \sum_{n=0}^{\infty} \frac{$a^n}{$b^{2n+1}} = \) \{ans_rule(20)\},
   41 $BR (d)  \( \displaystyle \sum_{n=5}^{\infty} \frac{$c^n}{$d^n} = \) \{ans_rule(20)\},
   42 $BR (e)  \( \displaystyle \sum_{n=1}^{\infty} \frac{$e^n}{$e^{n+4}} = \) \{ans_rule(20)\},
   43 $BR (f)  \( \displaystyle \sum_{n=1}^{\infty} \frac{$c^n +$a^n}{$d^n} = \) \{ans_rule(20)\}.
   44 
   45 EOT
   46 
   47 &ANS(std_str_cmp($ans0));
   48 &ANS(std_num_cmp($ans1));
   49 &ANS(std_num_cmp($ans2));
   50 &ANS(std_num_cmp($ans3));
   51 &ANS(std_str_cmp($ans0));
   52 &ANS(std_num_cmp($ans5));
   53 
   54 
   55 ENDDOCUMENT;
   56