Sum of First 100 Natural Numbers

If the qustion of sum of first 100 natural numbers is asked most people will readily answer as 5050 using n(n+1)/2 formula. When the same question was asked to Carl Frederick Gauss, the greatest mathematician ever lived, when he was barely 5 years old, he solved it in a most natural and ingenious way for a 5 year old. This method is a basic idea for deriving n(n+1)/2. Can you just imagine how he did it?

Answer:

First he (Gauss) imagined that he had written all the first 100 Natural numbers and started adding in the following way:

1+2+3+4+5+................................97+98+99+100

= (1+100)+(2+99)+(3+98)+(4+97)+..................(50+51)

=101 + 101 + 101 + 101 +.................. 101

= 101 summed 50 times, (because 100 numbers are paired into 50)

= 101 x 50 = 5050.

Truly remarkable for a tender 5 year old to conceive and devise such a marvellous and wonderful method.