Question

find the sum of first ñ odd natural numbers

Answer 1

We have no.of first odd no = n

Let the first odd numbers be x1 , x2 ......xn.

Thus , sum of first n odd numbers = sigma xn

Answer 2

solution :

To find ,

The sum of first n odd natural numbers

The odd natural numbers are ,

1,3,5,7........ ,n

These are in Ap

» a=1

d = 2

number of terms=n

Sum = n/2 [2a+ (n-1)d ]

substitute values,

n/2[2x1 + (n-1) 2 ]

n/2 [2+ (n-1)2]

=> n[1 + n -1 ]

=> n^2

Thus the sum of first n odd natural numbers is n square