The purpose for this forum is to provide help so that people can learn the material on their own. I know this is not the response you wanted. But, I am willing to help you solve these problems. I just wanted to let you know that statement is not really appropriate for this forum.

What is Formula (8)? I assume it is the definition of the general binomial coefficient. By definition:

For the second equation, we can use Pascal's Rule: .

Proof by induction: , so the formula holds when . Assume the formula holds for all positive integers up to .

So, by the principle of mathematical induction, the formula holds for all positive integers .