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

Tue Jul 1 19:29:13 2003 UTC (9 years, 11 months ago) by voloshin
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    1 #DESCRIPTION
2 #Limits of sequences
3 #ENDDESCRIPTION
4
5 #Keywords('Series ' ,'Limits')
6
7 DOCUMENT();
9 "PG.pl",
10 "PGbasicmacros.pl",
11 "PGchoicemacros.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