Expanding (5+x)/(2-x+x²) using binomial series

[burgerandcheese]

Because the binomial expansion only works for | x | < 1 are we supposed to assume that | x | < 1 in the expression above?
Thanks

 

[Deleted member 4993]

View attachment 12317

Because the binomial expansion only works for | x | < 1 are we supposed to assume that | x | < 1 in the expression above?
Thanks

Actually you are assuming:

|1 - x/2 * (x-1)| < ε where ε is a very small number ~0

 

[burgerandcheese]

|1 - x/2 * (x-1)| < ε where ε is a very small number ~0

Sorry, I don't understand. Why is that so?

 

[Deleted member 4993]

Sorry, I don't understand. Why is that so?

(1- δ)^-1 = 1 + δ + δ² + δ³....... when δ < 1

In your case,

δ = x/2 * (x-1)