Question

Find the sum of the first 2,000 positive integers (the numbers 1 through 2000).

Answer 1

According to Gauss, the formula to find the sum of a series is:

S=n(n+1)/2 where n is the number of terms in the series

Since n=2000, then:

S=2000(2000+1)/2

S=4002000/2

S=2001000

The famous mathematician Gauss had used this same method to find the sum of the digits 1 to 100 while in elementary school. So the sum of the first 2000 positive integers is 2,001,000