addition / recursion problem

[owen76]

If you wanted to add all numbers together from 1 to x (ex. 1+2+3+4+5...x) what is the best way? Mathmatically there are ways easier than adding them all up in order, but I am curious about the programming side. Are there better ways to do this problem besides the obvious answers of a) one loop that takes forever or b) the recursion solution?

[roswell1329]

Not that you should listen to me (I seem to have a problem with Basic Algebra), but I think this will work:

((n + 1) / 2) * ((n - 1) + 1)

or just:

((n + 1) / 2) * n

Incidentally, this should work for a consecutive series between any two numbers. Just replace the inner 1's with the smaller number. For example:

To add the series 4+5+6+7+8+9+10, the equation would be:

((10+4) / 2) * ((10 - 4) + 1)

Which should equal 49...the same answer to 4+5+6+7+8+9+10. Again, I think this will always work, but I'm not sure.

The algebraic equation to add all numbers between x and n:

((n + x) / 2) * ((n - x) + 1)