# Complex Analysis : Taylor and Laurent Series

## Example Questions

### Example Question #1 : Taylor And Laurent Series

Find the Taylor Series expansion of

Possible Answers:

Correct answer:

Explanation:

It is well known (can be shown by the definition) that that

Making the appropriate substitutions

Shifting the index of summation gives us

### Example Question #1 : Taylor And Laurent Series

Find the first three terms of the Taylor Series of

Possible Answers:

Correct answer:

Explanation:

Taylor Series expansion of the numerator and the denominator seperately gives us

A term by term multiplication gives us

Combining like terms