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  • No spreadsheet required...

    Imagine a triangle that's got rows of 1, 2, 3, 4 items:-

    o
    o o
    o o o
    o o o o

    Now imagine another triangle upside down that "fits" on top,

    o x x x x
    o o x x x
    o o o x x
    o o o o x

    This makes a rectangle of 4 x 5

    So to add up 1,2,3,4 you can do 4 * (4+1) / 2 = 4 * 5 / 2 = 10.

    In general that's n * (n+1) /2

    So for 31 you get 31 * 32 / 2 = 496km.

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