Find
$\sum_{r=0}^n3^r\binom{n}r$
When I tried to do it I got
$1 + 3n + 3^2\cdot \frac{n(n-1)}2 + \ldots + 3^{n-1}\cdot n + 3^n$
but I couldn't equate it to $4^n$ which is the answer I got by substituting $n$ for various numbers.
Can you tell me the correct mathematical way of getting the answer?