Sum of all numbers

Question

I need to write a function that calculates the sum of all numbers n.

Row 1:          1 
Row 2:         2 3 
Row 3:        4 5 6 
Row 4:       7 8 9 10 
Row 5:     11 12 13 14 15 
Row 6:   16 17 18 19 20 21 

It helps to imagine the above rows as a 'number triangle.' The function should take a number, n, which denotes how many numbers as well as which row to use. Row 5's sum is 65. How would I get my function to do this computation for any n-value?

For clarity's sake, this is not homework. It was on a recent midterm and needless to say, I was stumped.

Answer 1

The leftmost number in column 5 is 11 = (4+3+2+1)+1 which is sum(range(5))+1. This is generally true for any n.

So:

def triangle_sum(n):
    start = sum(range(n))+1
    return sum(range(start,start+n))

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As noted by a bunch of people, you can express sum(range(n)) analytically as n*(n-1)//2 so this could be done even slightly more elegantly by:

def triangle_sum(n):
    start = n*(n-1)//2+1
    return sum(range(start,start+n))