Question

What is the interval of convergence for the power series representation of f(x) = x/(1+6x) centered at x=0.

Answer 1

I know the series is a Maclaurin series and also how to find the interval of convergence using the ratio test. Where I'm having difficulty is finding a power series representation.

Answer 2

divide top and bottom by x, and then let the bottom be u

define the power series for u^(-1) and then reintroduce the x value.

something along those lines is in my head.

Answer 3

may or may not be valid ... ohohoh ... try to divide long hand

Answer 4

power series gets generated here
-----------
1 + 6x | x





x -6x^2 +6^2x^3 +- ....
-----------
1 + 6x | x
(x+6x^2)
-------
-6x^2
(-6x^2 -6^2x^3)
----------------
6^2 x^3

Answer 5

You have many examples in your textbook similar to your quest

Answer 6

Here is a hint: start by 1/(1+x) which you know

Answer 7

Then multiply by x. Here your r=-6x