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Reusable formula for decrementing denominator

  1. Sep 10, 2011 #1
    I am currently working on computer program that has to find the sum of during looping:

    1 + 1/2 + 1/3 + 1/4 + etc.

    So the loop looks something like this:

    sum = 1;
    counter = 2;

    sum = sum + (1/counter);
    counter = counter +1;

    My general question however is purely mathematical.

    I am currently using a basic counter variable to keep track of what the next denominator value will be, but I was hoping there was some formula I could be used to go from: 1/2 to 1/3, then 1/3 to 1/4. I am unable to find a consistent relationship between each value and the next in order to simplify my code. Any suggestions would be greatly appreciated.
  2. jcsd
  3. Sep 10, 2011 #2
    The relationship is nonlinear -- you can't find a common difference or ratio between each pair of adjacent terms. The relationship is as follows: if the term in question is [itex]1 \over n[/itex], then the following term will be [itex]1 \over n + 1[/itex]. It's not really like you can add or multiply some constant to get the next term in the sequence.
  4. Sep 10, 2011 #3
    What he said. Looks like you're using JavaScript or similar, so you can sacrifice some readability and shorten it to
    Code (Text):
    sum = 1;
    counter = 2;

    sum = sum + (1/counter++);
    The trailing ++ tells the compiler to add 1 to counter after the expression has been evaluated. That's about as simple as this code can get.

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