Sum with $3^k$

#binomial#power sum#3^k

Statement

Compute $\sum_{k=0}^{n}3^k\binom{n}{k}$ .

Hint

Binomial theorem with $a=1$ , $b=3$ .

Show solutionHide solution

Binomial theorem. $(1+3)^n=4^n=\sum_k\binom{n}{k}3^k$ .

Conclusion. $\sum_k 3^k\binom{n}{k}=4^n$ .