"Compute $\sum_{j=0}^m 3^j {m \choose j}$
The result should be somewhat familiar. Then, use the binomial theorem to verify the result."
I'm having some serious trouble with this problem. I'm not sure how to start computing.
What is the first step here?
Hint. If you know the binomial theorem, it may be easier to apply to the following rewriting of your expression:
$$ \sum_{j=0}^m \binom{m}{j} 3^j 1^{m-j} $$
I'm not sure how you are expected to arrive at the general result without the binomial theorem, though. Maybe you are supposed to just evaluate the expression for selected values of $m$, and observe the obvious pattern?