Using induction to prove that the sum formula works for any term

The video tutorial explains how to prove a sum formula using mathematical induction. It begins with verifying the base case, showing that the sum of the first term is correct. The instructor then moves on to the inductive step, demonstrating how to prove the formula for any term K and its subsequent term K+1. The tutorial includes simplification of expressions and concludes by confirming the validity of the sum formula through properties of exponents.

How is the sum for K + 1 derived from the sum for K?

What conclusion is drawn about the sum formula at the end of the text?