Question

find the sum of first n odd natural numbers.

Answer 1

Answer:

The sum of first n odd natural numbers are n²

Step-by-step explanation:

Given :  

odd natural numbers are 1, 3 , 5 ……….

a = 1, d = 3 - 1 = 2

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

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

Sn = n/2  [2  + 2n – 2]

Sn = n/2 × 2 [1  + n – 1]

Sn = n [ n ]

Sn = n²

Hence, the sum of first n odd natural numbers are n²

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Answer 2

Answer:

odd numbers = 1+3+.......2n-1

= ( 1+2+3+.....+2n)

- 2+4+6+.....+2n)

$\frac{2n(2n + 1)}{2} - \frac{2n(n + 1)}{2}$

= (2n²+n) - (n² +n)

= n²

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