Python - sum of numbers

Question

I am trying to sum all numbers to a range, with all numbers to the same range.

I am using python:

limit = 10
sums = []
for x in range(1,limit+1):
    for y in range(1,limit+1):
        sums.append(x+y)

This works fine, however, due to nested loops, if the limit is too large, it will take a long time to calculate the sums.

Is there a way to do this without a nested loop?

(This is simply a simplification of what I need to do to solve the ProjectEuler problem. It involves getting the sum of all the bountiful numbers.)

Answer 1

[x + y for x in xrange(limit + 1) for y in xrange(x + 1)]

It does the same amount of calculations anyway, but will do it about twice as fast as the for loop.

from itertools import combinations

(a + b for a, b in combinations(xrange(n + 1, 2)))

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:

 [x + y for x in set set1 for y in set2]

Answer 2

, .

, limit**2.

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Answer 3

, .

, :

[x + y x (1, + 1) y (1, + 1)]