Geometric power series of f(x)=6/(2-x) c=1

[NIZBIT]

Find the geometric power series for the given function:

f(x)=6/(2-x) c=1

I am stumped on this one. I've tried for an hour on this one with no luck. Could someone help?

 

[courtrigrad]

Write it as $$6\left(\frac{1}{2-x}\right)$$. You have to get rid of the 2 so write it as follows:

$$6\left(\frac{1}{2(1-\frac{x}{2})}\right) \rightarrow 3\left(\frac{1}{1-\frac{x}{2}}\right)$$