Question

the region of validity of 1/1+z Of Taylor's Series expansion about z=0​

Answer 1

Answer:

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Answer 2

For a function  f(z)=$\frac{1}{z}$  does not have the region of validity at  z=0 .

To prove the above statement we will suppose that it did ,

Then inside of a region around  z=0 would be given by the formula

$\frac{1}{z}$ =$a_{0} + a_{1} z^{1} + a_{2} z^{2} +a_{3} z^{3} + ...$

and if we choose some  z≠0  inside of that area or region , We will have to multiply the above equation with z ,

We get

1 = $a_{0}z + a_{1} z^{2} + a_{2} z^{3} +a_{3} z^{4} + ...$

This quantity can be true for a finite number of z , but it can’t be true for region inside inside . So the equation is false for this particular case.

Hence the region of validity is not available in this case.