Question

Prove that the sum of the first n odd numbers is n2

Answer 1

Proving by example


Sum of first 3 odd numbers is 3²=9

First 3 odd numbers are 1+3+5=9

Hence ,Sum of first n odd natural numbers is n²

Hope helped !

Answer 2

We have,

First n odd numbers =

1,3,5,7,9 . . .upto n terms .

No doubt,it forms an A.P.

here first term = 1

and,common difference = 2.

thus, sum of n terms of this A.P. = n/2[2a + (n - 1 )d ]

= n/2[2 + 2n - 2]

= n².

Hence proved.