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).

Question

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).

anonymous · Answer

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

anonymous · Answer

Does it at least make some sense?

anonymous · Answer

You would have to multiply the summation by 3.

anonymous · Answer

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

anonymous · Answer

*
actually 1/3

anonymous · Answer

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

anonymous · Answer

I missed that

anonymous · Answer

it is one of those little errors.

anonymous · Answer

So Does it make sense now WRosa?

anonymous · Answer

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

anonymous · Answer

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