text: ## DESCRIPTION
  ## Calculus
  ## ENDDESCRIPTION
  
  ## Tagged by cmd6a 6/1/06
  
  ## DBsubject(Calculus - single variable)
  ## DBchapter(Infinite sequences and series)
  ## DBsection(Interval of convergence of a power series)
  ## Institution(OSU)
  ## Level(4)
  ## KEYWORDS('calculus','power series','radius of convergence')
  
  DOCUMENT();        # This should be the first executable line in the problem.
  
  loadMacros(
    "PGstandard.pl",
    "PGchoicemacros.pl",
    "PGcourse.pl"
  );
  
  TEXT(beginproblem());
  $showPartialCorrectAnswers = 1;
  
  $a = random(2,9,1);
  $b = $a;
  while ($b == $a) { $b = random(2,9,1) };
  $c = random(2,5,1);
  $d = random(1,9,1);
  $e = random(1,9,1);
  $f = non_zero_random(-5,5,1);
  
  $g_numb = random(2,9,1);
  $g_sign = random(-1,1,2);
  $g      = $g_numb * $g_sign;
  
  $h = non_zero_random(-9,9,1);
  
  TEXT(EV2(<<EOT));
  Define the double factorial of \( n \), denoted \( n!! \), as follows:
  \[ n!!  = \begin{cases} 
       1 \cdot 3 \cdot 5 \cdot \cdot \cdot \cdot (n-2) \cdot n \quad \text{ if } n \text{ is odd} \\
       2 \cdot 4 \cdot 6 \cdot \cdot \cdot \cdot (n-2) \cdot n \quad \text{if } n \text{ is even} \end{cases} \]
  
  where \( (-1)!! = 0!! = 1 \).
  $PAR
  Find the radius of convergence for the given power series.
  \[ \sum_{n=1}^\infty \frac
      { $a^n \cdot n! \cdot ($c n + $d)! \cdot (2n)!! }
      { $b^n \cdot [(n + $e)!]^$c \cdot (4n + $f)!!} ($g x + $h)^n \]
  
  $BR
  $BR
  The radius of convergence, \(R =\) \{ ans_rule(20)\}
  EOT
  
  $ans1 = 8 * $b / ($a * $g_numb * $c**$c);
  
  ANS(num_cmp($ans1));
  
  ENDDOCUMENT();        # This should be the last executable line in the problem.
  