Question: Find the generating series with the property that for each non-negative integer $n$, the coefficient of $x^n$ is the number of "words" of length $n$ coming from the alphabet $\{{a,b,c}\}$. Examples of words of length 3 are aaa, aab, baa, cba, etc.
So I believe this means you could choose anywhere from $0$ to $n$ numbers from the "alphabet", and the number of combinations for any length $n$ would just be $3^n$ for $n>0$. So would the coefficients simply be $3^n$? Would this yield: $\sum_{n=1}^33^nx^n $ ? This seems too incorrect, any help would be much appreciated.
On a side note, the question goes on to solve for the general case of any alphabet size $k$, where $k$ is any positive integer.