# Math

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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 -

901

• Math -

you get 5050

• Math -

5050

• Math -

The formula for calculating the sum of consecutive number is
S = n*(a1 + an) / 2
where
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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