Chapter 5, Problem 7E

To determine

To prove: The $3^n={\displaystyle \sum _{k=0}^n\left(\begin{array}{l}n\\ k\end{array}\right)2^k}$ by using the binomial theorem and generalize to find sum of ${\displaystyle \sum _{k=0}^n\left(\begin{array}{l}n\\ k\end{array}\right)r^k}$ for any real number r.