# Math Help - Need help with power series form

1. ## Need help with power series form

2. Hint :

Use:

(i) g ( x ) = 1 / (x - 2 ) = ( -1 / 2 ) ( 1 + x / 2 + x^2 / 4 + ... ) ( if | x | < 2 )

(ii) g' ( x) = - 1 / ( x - 2 )^2

3. Note that , so if you find the power series for , differentiate it term by term. Then multiply it all by .

4. Ah thank you so much. I thought we had to integrate it all this time.