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  4. If B is a natural number and it can be expressed as the sum of the first A consecutive odd natural numbers, then the value of B-A2 is

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Q. If $B$ is a natural number and it can be expressed as the sum of the first $A$ consecutive odd natural numbers, then the value of $B-A^2$ is __

Squares and Square Roots and Cubes and Cube Roots

Solution:

Given $B$ is a natural number.
The sum of the first $A$ consecutive odd numbers required to give the sum equal to $B$.
$\therefore A^2=B$ (successive subtraction method)
$\therefore B-A^2=0$