Power Series Calc 2: Determine 1/(1+9x)^2 From n=1 to ∞

[andy727]

Homework Statement

Determine the power series for g(x)=1/(1+9x)^2
The sigma in the answer has to be from n=1 to infinity
We also have to specify whether it is alternating by putting either (1)^n or (-1)^n

This is an online problem and I have no idea why what I am putting is not right

Homework Equations

1/(1-u) = [sigma from n=0 to infinity (u^n)]

The Attempt at a Solution

g(x)=1/(1+9x)^2 = 1/(1+18x+81x^2) = 1/(1-(-18x-81x^2))

1/(1-u) = [sigma from n=0 to infinity (u^n)]

g(x) = sigma from n=0 to infinity(-18x-81x^2)^n
= sigma from n=0 to infinity ((-1)^n*(18x+81x^2)^n)
= sigma from n=1 to infinity ((-1)^n*(-1)*(18x+81x^2)^(n-1))

 

[Whitishcube]

If you're entering this into an online program, it may not accept the form of your solution. Try writing something that's equivalent to your expression but slightly different (or simpler).