Question

Probably an easy one, but how to expand f(x)=1/(8-x) in Taylor series?

Answer 1

1/(1-x) = 1 + x + x^2 + x^3 + ....

Convert your expression into something like 1/(1-x) and then use this result.

Answer 2

hmm, so if I take 1/8 * (1/(1-x/8) it works fine and in that classic series that You posted I just put 1/8th in front of everything, and instead of x I have x/8 ?

Answer 3

yes

Answer 4

This is the fast way to derive the Taylor Series.

But it's a good exercise to calculate the Taylor Series explicitly for a few terms to convince yourself you arrive at the same answer.