Taylor Series of 1/w: Proving Convergence

[jm915]

Homework Statement

Find the Taylor Series for f(w) = 1/w centered at w0 = 1 using 1/w = (1/1 + (w-1)). Show that the series converges when |w-1| < 1

Homework Equations

use 1/w = (1/1 + (w-1))

The Attempt at a Solution

 

[annoymage]

$$\frac{1}{1+x}$$ = $$\sum$$(-1)ⁿxⁿ

you know this right?