Question

the sum of n natural number is a three digit number all of whose digits are same . what is the value of n ?​

Answer 1

Answer:

In 5 seconds you can solve the equation 2n(n+1)=aaa (111, 222, etc) 

2n(n+1)=aaa=a×111=a×3×37 ⇒n(n+1)=6ax37

The L.H.S of the equation n(n + 1) is a product of two consecutive

natural numbers Therefore R.H.S. should also be a product of two

consecutive natural numbers One of the numbers is 37 Therefore  the other number,  6a consecutive to 37  can only be 36 giving a = 6 and n = 36 

Therefore 36 numbers have been summed up and their sum

is equal to 666