[rochester] / trunk / rochester_problib / setSeries1Definitions / ur_sr_1_4.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Annotation of /trunk/rochester_problib/setSeries1Definitions/ur_sr_1_4.pg

 1 : sam 2 #DESCRIPTION 2 : # Series. Find sum 3 : #KEYWORDS('Series' , 'Partial Sums' ) 4 : #ENDDESCRIPTION 5 : 6 : DOCUMENT(); # This should be the first executable line in the problem. 7 : 8 : loadMacros( 9 : "PG.pl", 10 : "PGbasicmacros.pl", 11 : "PGchoicemacros.pl", 12 : "PGanswermacros.pl", 13 : "PGauxiliaryFunctions.pl" 14 : ); 15 : 16 : TEXT(&beginproblem); 17 : $showPartialCorrectAnswers = 1; 18 : 19 :$a = random(2,10,1); 20 : $b = random(1,10,1); 21 : 22 :$d = 4; 23 : $e = 8; 24 : 25 : # Sum first d terms: 26 :$i = 0; 27 : $sumA = 0; 28 : while ($i < $d ) { 29 :$i = $i + 1; 30 :$fofi = $a/($b+$i); 31 :$sumA = $sumA +$fofi; 32 : } 33 : 34 : # Add on more to get sum of first e terms: 35 : $sumB =$sumA; 36 : while ($i <$e ) { 37 : $i =$i + 1; 38 : $fofi =$a/($b+$i); 39 : $sumB =$sumB + $fofi; 40 : } 41 : 42 : # OK, now we're ready for the problem: 43 : 44 : 45 : BEGIN_TEXT 46 : Consider the series 47 : voloshin 576 $$\displaystyle \sum_{n=1}^{\infty} \frac{a}{n + b}$$. 48 : sam 2 Let $$s_n$$ be the n-th partial sum; that is,$BR 49 : $s_n = \sum_{i=1}^n \frac{a}{i + b} .$ $BR 50 : Find $$s_{d}$$ and $$s_{e}$$$BR 51 : $$s_{d}$$ = \{ans_rule(40)\} $BR 52 : $$s_{e}$$ = \{ans_rule(50)\} 53 : END_TEXT 54 : 55 : &ANS( std_num_cmp($sumA) ); 56 : &ANS( std_num_cmp(\$sumB) ); 57 : 58 : ENDDOCUMENT(); # This should be the last executable line in the problem.