Given the series , calculate its region of convergence and the function it represents.
Attempt: for . Which is equal to . The radius of convergence is 10, so the region is a disk (without the border) centered at 0 with radius 10. Is that good?
2)Is a Laurent series of a function? Why?
Attempt: No, it isn't. Because which would be equal to . The problem is that for and for . Since the modulus cannot be greater and lesser than 1 at a time, the series doesn't converge to any function. (Yeah I know, I didn't prove it well. How would you solve the exercise?)