I know that the sum of power of 22 is 2n+1−12n+1−1, and I know the mathematical induction proof. But does anyone know how 2n+1−12n+1−1 comes up in the first place.
For example, sum of n numbers is n(n+1)2n(n+1)2. The idea is that we replicate the set and put it in a rectangle, hence we can do the trick. What is the logic behind the sum of power of 22 formula?