Parent Directory
| 
Revision Log
Revision 576 - (view) (download)
| 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. |
| aubreyja at gmail dot com | ViewVC Help |
| Powered by ViewVC 1.0.9 |