Thread: taylor series

derive taylor series representation for f(z)=1/1-z for |z-i|<squareroot of 2..ie..

1/1-z=summation n=0 to infinity (z-i)^n/(1-i)^n+1

Originally Posted by durham2

derive taylor series representation for f(z)=1/1-z for |z-i|<squareroot of 2..ie..

1/1-z=summation n=0 to infinity (z-i)^n/(1-i)^n+1

The easy way is to note that:

1.


.


2. .


Now recall the formula for the sum of an infinite geometric series.