How do I get the Math equation of Python Algorithm?

Question

ok so I am feeling a little stupid for not knowing this, but a coworker asked so I am asking here: I have written a python algorithm that solves his problem. given x > 0 add all numbers together from 1 to x.

def intsum(x):
  if x > 0:
    return x + intsum(x - 1)
  else:
    return 0

intsum(10)
55

first what is this type of equation is this and what is the correct way to get this answer as it is clearly easier using some other method?

Answer 1

This is recursion, though for some reason you're labeling it like it's factorial.

In any case, the sum from 1 to n is also simply:

n * ( n + 1 ) / 2

(You can special case it for negative values if you like.)