Question

What is the sum of first 'n' odd positive integers?

Answer 1

The sum of the first n even positive integers is p and the sum of the first n odd integers is q.

Answer 2

The sum of first 'n' odd positive integers is n²

Given: First 'n' odd positive integers

To Find: The sum of first 'n' odd positive integers

Solution:

The first 'n' odd natural numbers are = 1 , 3 , 5 , 7 , 9 ,..., ((2n-1)

We can clearly see that this forms an arithmetic progession (AP).

 a = 1, d = 2, tn = 2n - 1

The formula for sum of an AP is;

   S = n/2 [ 2a + ( n - 1 )×d ]

Putting the respective values, we get;

⇒ S = n/2 [ 2 + 2n - 2 ]

⇒ S = n/2 [2n]

⇒ S = n²

Hence the sum of first 'n' odd positive integers is n²

#SPJ3