How would I code this infinite series to carry on?

Just purely out of interest (and I'm sure the technique applied would come in handy in the开发者_开发百科 future)

How would one code the infinite series 1 + 1/2 +1/4 + 1/8... ad infinitum as an actual sum in c#? (I'm sure the word recursive or recursively could be used there somewhere)

Using lazy evaluation you can actually define(but not evaluate) an infinite sequence:

IEnumerable<double> Series()
{
  double sum=0;
  double element=1;
  while(true)
  {
    sum+=element;
    yield return sum;
    element/=2;
  }
}

Of course this is limited by rounding errors and thus will stop growing after about 53 iterations.

You could define it recursively, but I see no reason to do that:

double Series(int n)
{
  if(n==0)
    return 1;
  else
    return Math.Power(0.5,n)+Series(n-1);
}

var val = 0.0;
var sum = 1.0;
while(true)
{
  val += sum;
  sum /= 2;
}

You could use decimal datatype as it supports more decimal places than double. This can be done recursively or with a loop; I would recommend with a loop like so:

// endValue is an input integer 
decimal acc = 0.0m;
int factor = 1;
for (; factor < endValue; factor *= 2)
{
    try
    {
        acc += (1.0m/(decimal)factor);
    }
    catch
    {
        // we've exceeded bounds of the datatype; return last result
    }
}
return acc;

Building on the idea presented by CodeInChaos you could create

static IEnumerable<T> Series<T>(Func<T,T> function, 
                                   T seed, 
                                   int interations = int.MaxValue)
{
    T value = seed;

    for (int i = 0; i < iterations; i++)
    {
        value = function(value);
        yield return value;
    }
}

and

    static IEnumerable<T> Series<T>(Func<T, int, T> function, 
                                   T seed, 
                                   int interations = int.MaxValue)
{
    T value = seed;

    for (int i = 0; i < iterations; i++)
    {
        value = function(value, i);
        yield return value;
    }
}

allowing you to iteration over any series you like, such as:

double total = 0;
double newTotal = 0;
foreach (double v in Series(v => v * .5, 1.0, 100))
{
    newTotal += v;
    Console.WriteLine(total);
    if (total == newTotal) break;
    total = newTotal;
}