Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

what do you get when you add all of the numbers from 1 to 100?

what do you get when you add all of the numbers from 1 to 100?

7 Answers

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  • 1 decade ago
    Favorite Answer

    You pair them off:

    1+99 = 100

    2 + 98 = 100

    3 + 97 = 100

    ...

    48+52 = 100

    49 + 51 = 100

    That's 49 pairs of 100. We accounted for everything but the 50 and the 100. So 49*100+100+50 = 5050.

    This is a problem famously solved by C.F. Gauss when he was a child. See:

    http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#...

    There is a general formula for this:

    http://en.wikipedia.org/wiki/Arithmetic_series#Sum...

    1 + 2 + ... + n = n(n+1) / 2

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  • frank
    Lv 7
    1 decade ago

    Sn = n(n + 1)/2

    with 1 + 2 + 3 +... + n

    So, 1 + 2 + 3 + ... + 100 => 100(101)/2 = 5050

    Answer : 5050

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  • 1 decade ago

    it is A.S a=1,l= 100 ,n=100 then sum = n/2 (a+ l) then

    sum = 100/2 (1+100)=5050

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  • 1 decade ago

    You have 100 numbers.

    Average = 101/2 = 50.5

    50.5 x 100 = 5,050

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  • Anonymous
    1 decade ago

    5050

    the formula you can use to calculate "n" for any number is

    1/2n^2+1/2n

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  • 1 decade ago

    5050, just like Gauss did!

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  • 1 decade ago

    5,050.

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