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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1688 byte(s)
Rogawski problems contributed by publisher WHFreeman. These are a subset of the problems available to instructors who use the Rogawski textbook. The remainder can be obtained from the publisher.

    1 ## DBsubject('Calculus')
2 ## DBchapter('Infinite Sequences and Series')
3 ## DBsection('Infinite Sequences and Series')
4 ## KEYWORDS('calculus', 'series')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('10.1')
9 ## Problem1('9')
10 ## Author('LA Danielson')
11 ## Institution('The College of Idaho')
12
13 DOCUMENT();
17
18 Context()->texStrings;
19
20 sub harmonic_sum {
21     $n = shift; 22$sum = 0;
23
24     for($i=1;$i<=$n;$i++){
25       $sum += 1/$i;
26     }
27
28 #    $ret_val =$sum;
29
30     return $sum; 31 } 32 33$a = Real(random(2,9,1));
34
35 $c1=$a*harmonic_sum(1);
36 $c2=$a*harmonic_sum(2);
37 $c3=$a*harmonic_sum(3);
38 $c4=$a*harmonic_sum(4);
39
40 BEGIN_TEXT
41 \{ beginproblem() \}
42 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","9") \}
43 $PAR 44 Calculate the first four terms of the following sequence, starting with $$n=1$$. 45 46 $c_n=a+\frac{a}{2}+\frac{a}{3}+\ldots+\frac{a}{n}$ 47 48 $$c_1 =$$ \{ans_rule()\}$BR
49 $$c_2 =$$ \{ans_rule()\}$BR 50 $$c_3 =$$ \{ans_rule()\}$BR
51 $$c_4 =$$ \{ans_rule()\}$BR 52 END_TEXT 53 Context()->normalStrings; 54 55 ANS($c1->cmp);
56 ANS($c2->cmp); 57 ANS($c3->cmp);
58 ANS($c4->cmp); 59 60 Context()->texStrings; 61 SOLUTION(EV3(<<'END_SOLUTION')); 62$PAR
63 $SOL 64 Setting $$n=1,2,3,4$$ in the formula for $$c_n$$ gives$BR
65 $$c1=c1$$$BR 66 $$c2=a+\frac{a}{2}=a\left(\frac{3}{2}\right)=c2$$$BR
67 $$c3=a+\frac{a}{2}+\frac{a}{3}= a\left( \frac{11}{6}\right)=c3$$\$BR
68 $$c4=a+\frac{a}{2}+\frac{a}{3}+\frac{a}{4}=a\left( \frac{25}{12}\right) = c4$$
69 END_SOLUTION
70
71 ENDDOCUMENT();