## anonymous 5 years ago How to solve: Use geometric series 1/(x+1) = Summation (n=0 to infinity) (-1)^n * x^n, to find the power series representation of f(x) = 1 / (4x +3).

1. anonymous

F(x)=1/(x+1) can be represented as $\sum_{0}^{infiniti}(-1)^n x^n$ F(x)=1/(4/3x +1) is same as f(x)=1/4x+3 So you would substitute in 4/3x in place of x

2. anonymous

Does it at least make some sense?

3. anonymous

You would have to multiply the summation by 3.

4. anonymous

1/3(4/3x+1) you can factor out 1/3

5. anonymous

* actually 1/3

6. anonymous

Yes you factor out the 1/3 but you did not account for it.

7. anonymous

I missed that

8. anonymous

it is one of those little errors.

9. anonymous

So Does it make sense now WRosa?

10. anonymous

$1/3\sum_{0}^{\infty} (-1^n)(4/3x)^n$

11. anonymous

So the solution is: f(x) = 1/(4x+3) f(x) = 1/3 ((4/3)x + 1) $1/3 \sum_{n=0}^{\infty} (-1)^{n} ((4/3)x)^{n}$