Determine the Laurent series for $f(z)=\frac{1}{z(z+5)}$ valid in the region$ \{z: |z| < 5\}$
When i expand i got,
$f(z)= \sum_{n=0}^{\infty}\frac{(-1)^nz^{n-1}}{5^{n+1}}$. But Contour here is circle with center 0, radius 5.
But simple poles are 0, -5. O is inside given region C:$|z|<5$. Laurent series expansion pre-condition, f(z) analytical through out within C(is it on C? - i have a doubt here). So is this expansion valid???? - No i think. Pls correct me if i am wrong