Question

For instance let’s say I want to sum up all x^2 (or any other arbitrary function) for x=1 onward until x^2 is greater than n. Can this be done without using a bunch of while loops and if-checks?

Answer 1

The itertools modules has some nice functions for an extensible solution:

from itertools import takewhile, count

def sum_func(func, n):
    return sum(takewhile(lambda x: x < n, (func(i) for i in count(1))))

For example:

>>> sum_func(lambda x: x**2, 20)  # 1^2 + 2^2 + 3^2 + 4^2
30

If you want to make this also work with decreasing functions, you could also just pass in the test function:

def sum_func(func, pred):
    return sum(takewhile(pred, (func(i) for i in count(1))))

Example:

>>> sum_func(lambda x: -x*2, lambda x: x > -10)  # -1*2 + -2*2 + -3*2 + -4*2
-20