Question

Evaluate :

Answer 1

\[\sum_{r=0}^{n} n c_{r} 3^{n-r}\]

Answer 2

What is \(c_r\)? Maybe you mean \({}_nC_{r}\), as in "\(n\) choose \(r\)" or \(\dbinom nr\)?

If that's the case, then
\[\sum_{r=0}^n \binom nr 3^{n-r}=\sum_{r=0}^n \binom nr 3^{n-r}\color{red}{1^r}=(3+1)^n\]
by the binomial theorem.