Reusable formula for decrementing denominator

[KevinMulito]

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;

while(...){
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.

 

[Dr. Seafood]

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 $1 \over n$, then the following term will be $1 \over n + 1$. It's not really like you can add or multiply some constant to get the next term in the sequence.

 

[Nowhere Man]

What he said. Looks like you're using JavaScript or similar, so you can sacrifice some readability and shorten it to

sum = 1;
counter = 2;

while(...){
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.

Fred