Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle $C$ in the complex plane is/are TRUE?

Let $z$ be a complex variable. If $f(z)=\frac{\sin(\pi z)}{z^{2}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint\limits_{C} f(z)dz$ is _______.

Consider the following series :

$$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}} $$

For which of the following combinations of c, d values does this series converge?