Power Series Representation of a Function Help

[DCASH88]

1. Homework Statement : Find the power series for the function f(x)=5/(7-x), centered at c=-2.
2. Homework Equations : a/(1-r)
3. The Attempt at a Solution : I know that I need to divide by seven to get (5/7)/(1-(x/7)) and then rewrite in the form the sum of (a)(r)^n. I tried adding 2 to x/7 so i had the sum of (5/7)((x/7)+2)^n from 0 to infinity but this was wrong. The professor wrote that the correct answer is the sum of 5(x+2)^n/9^(n+1) from 0 to infinity but I don't know how to get to that answer mainly because I don't know how to account for it being centered at -2 any help would be appreciated.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Dick]

You want to express it as a power series in powers of (x+2), that's how you center it at x=-2. 5/(7-x)=5/(9-(x+2)). Try expanding the second form.

 

[DCASH88]

Thank you that was very helpful

Daniel