Okay, I got help and figured out that I should use the form:
So then I got to:
and
Now, I figured out that the radius of convergence is 10, but I'm still unsure for the coefficients.
I am given:
And it says to find the first few coefficients, c0,c1...,to c4, which I can't find. Then it says to find the radius of convergence R of the power series. I'm not sure why they have the fraction equaling the series. I know I can use the ratio or root test to find the radius of convergence, but what exactly is the above problem stating?
Thanks,
Matt
Hello, matt3D!
Use long division . . .
(a) Find the first few coefficients, to
(b) Find the radius of convergence R of the power series.
We see that: .
(a) The first five coefficients are: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
The general term is: . . . . for
Ratio Test: .
And we have: .
(b) Therefore, the radius of convergence is: .