- #1

- 124

- 0

## Homework Statement

a) determine where f(z) is analytic.

f(z) = sum from n to inf. [ ( (-1)^n * n^2 ) / ( 2^n ) * (z - 6)^n ]

b) evaluate f'''(6)

## Homework Equations

ratio test

## The Attempt at a Solution

a) I used the ratio test and found that f(z) is analytic on the circle of convergence C: | z - 6 | < 1/2.

b) I found the 3rd derivative of the sum as

f'''(z) = sum from 0 to inf [ ( (-1)^n * n^2 ) / ( 2^n ) * n * (n-1) * (n-2) * (z - 6)^(n-3) ]

then when i plug in 6 into this i get

f'''(6) = 0

any suggestions or comments are much apperciated. thanks