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1+2+3+4+5+...100=?

5050 123 889 988 0 989

Chris Li by Chris Li , 21, China

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2 solutions

Galen Buhain
Jul 30, 2015

50*101=5050

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Jake Lee
Jan 29, 2015

This is the same question that a mathematics teacher gave the child prodigy Carl Friedrich Gauss during his time in school, the idea was that the students would take a long time to complete the question so that the teacher could have a nap.

Gauss noted that the sum of the start and end term of the addition is 101, and likewise the second and second-last term is 101 also. He realised that there are 50 such pairs in the addition all with the sum of 101. So he multiplied 101 by 50 to get the answer 5050.

We can use the formula:

Sum of n (from 1 to n) = n/2 * (n+1)

We have 100 terms so we have:

50 * 101 = 5,050

The same result as Gauss derived and calculated in his maths class.

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