Geometric progression is the progression in which every next term is found by multiplying the previous term by a fixed number. In other words, we can say that it is the progression in which any term divided by previous term always remain constant. Lets take an example of geometric progression.
A natural number m is called a perfect square number if it can be expressed as where n is also a natural number. For example, 4 is a perfect square number because it is a natural number and it can be expressed as and 2 is also a natural number.
We have a property
Can we easily find the value of using the above property?
If you want to recall what are perfect square numbers then please refer to my article on What are the perfect square numbers. This article asks a question that how many natural numbers lie between two consecutive perfect square numbers. You can also ask the same question as how many non-perfect square numbers lie between two consecutive perfect square numbers? Can we come up with a general formula for that?