Question: which of the following are correct check all that...

Which of the following are correct? ( Check all that apply)

a. The Laurent series representation of the function

f (z) = \frac{1}{z - 2}

in the annulus

{| z - 2 | > 0}

\sum_{n = 1}^{\infty} 2^{n - 1} \frac{1}{(z - 2)^{n}}

b. The Laurent series representation of the function

f (z) = \frac{1}{z - i}

in the annulus

{| z | > 1}

\sum_{n = 1}^{\infty} i^{n - 1} \frac{1}{z^{n}}

c. The Laurent series representation of the function

f (z) = \frac{1}{z + 1}

in the annulus

{| z | > 1}

\sum_{n = 1}^{\infty} (- 1)^{n - 1} \frac{1}{(z + 1)^{n}}

d. The Taylor series representation of the function

f (z) = \frac{1}{z + 1}

in the disk

{| z | < 1}

\sum_{n = 0}^{\infty} (- 1)^{n} z^{n}