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If I add all the numbers from 1-100 what do I get? This question has been confusing me for a while...

  • Math -


  • Math -

    you get 5050

  • Math -


  • Math -

    The formula for calculating the sum of consecutive number is
    S = n*(a1 + an) / 2
    n = number of terms
    a1 = first number
    an = last number
    Since it is from 1 to 100, n = 100. Substituting,
    S = 100*(1+100)/2
    S = 5050

    Hope this helps~ :)

  • Math -

    You can also do it quickly as Gauss discovered when he was a child.

    Consider all the numbers as if written in two lines.
    1-50 ascending
    100-51 descending

    adding the two numbers that are in the same positions, each pair makes 101. There are 50 such pairs, so the sum is 5050.

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