Conjecture

 

Vande Matram! Note this down.

 

The sum of the first n odd positive numbers is equal to n².

Let’s prove this

1^stpositive odd number is 1 = 1².
Sum of first two positive odd numbers is: 1 + 3 = 4 = 2².
Sum of first three positive odd numbers is: 1 + 3 + 5 = 9 = 3².

And so on.

Let’s find sum of the first ten positive odd numbers:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100 = 10².

Thus it is proved that the sum of the first n odd positive numbers is equal to n².

Such a rule is called “conjecture”.

Thanks for noting. Let me know your questions in the comments.