  In this article, we present four issues and provide a creative and concise
proof for each of them. The four issues are:
  1- Inequality
$\frac{1}{\sqrt{n\pi+\frac{\pi}{2}}}<\frac{\binom{2n}{n}}{2^{2n}}<\frac{1}{\sqrt{n\pi}}$
  2- A special case of Jonathan Wilde's problem
  3- Combination series
  4- A feature of powerful numbers.
