### Brain Teasers

# A History Lesson

When Carl Friedrich Gauss was six years old (back in 1783), his schoolteacher asked the students to add up all the numbers from 1 to 100. Unfortunately for the teacher, who was hoping to keep the class occupied, it took young Gauss only a few seconds to work out the answer. Can you figure out what Gauss did to come up with the answer?

### Hint

There is a pattern...### Answer

Gauss realized that the series 1+2+3+4...+97+98+99+100 could be written as 1+100+2+99+3+98+4+97... or 101 times 50 to get the total 5,050.This trick works for any sum of sequential integers. The general formula is n(n+1)/2, which is the equation for triangular numbers.

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