Let $\gamma$ be the circular contour, positively oriented, with centre $0$ and radius $7$. Let $A$, $B$ and $C$ be complex numbers. Compute the following integral $$\int_{\gamma } \frac{A+Bz+Cz^2}{z^n} dz.$$
I have no clue where to start with this question if anybody could help me.
Hint. Recall that the residue at $0$ of a function $f$ is the coefficient of $1/z$ in the Laurent series expansion of $f$ centered at $0$. In this case, the given function is already expanded and therefore, by the Residue Theorem, $$\frac{1}{2\pi i}\int_{|z|=7 } \frac{A+Bz+Cz^2}{z^n} dz=\begin{cases} A&\text{if $n=1$,}\\ ?&\text{if $n=2$,}\\ ?&\text{if $n=3$,}\\ 0&\text{otherwise.}\\ \end{cases}$$ Are you able to complete the evaluation?