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 thesame 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.

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 splendid method.