# Help expressing a function as a power series

• October 11th 2008, 01:05 PM
paulrb
Help expressing a function as a power series
Find the power series for (2+x)^(-3)

I'm pretty sure I'm supposed to use a binomial series, but the formula for that is (1+x)^k. Since I have (2+x)^k, all I can think of is replacing x with u = x+1, and find (1+u)^(-3). Is this correct? I'm getting stuck in the middle of the problem using this method.
• October 11th 2008, 02:15 PM
Moo
Hello,
Quote:

Originally Posted by paulrb
Find the power series for (2+x)^(-3)

I'm pretty sure I'm supposed to use a binomial series, but the formula for that is (1+x)^k. Since I have (2+x)^k, all I can think of is replacing x with u = x+1, and find (1+u)^(-3). Is this correct? I'm getting stuck in the middle of the problem using this method.

More simply :

$2+x=\frac 12 (1+\tfrac x2)$

So $(2+x)^{-3}=8 (1+\tfrac x2)^{-3}$

get it ?
• October 11th 2008, 03:54 PM
paulrb
Ok, that makes it much easier. Thanks.