Find a Power Series Representation for the function and determine the interval of convergence.

Question

anonymous · Answer

$$f(x)= \frac{ 1+x }{ 1-x }$$

amistre64 · Answer

youll want to start by calculating a few of the derivatives of it

anonymous · Answer

Low de High - High De Low???

amistre64 · Answer

sounds about right :)  or you can up the bottom and just run the product rule

anonymous · Answer

but then i will still get a fraction... how will i be able to express as a power series

amistre64 · Answer

the derivatives act as the constant terms of all the power terms of the polynomial; if we can spot a pattern we can develop a rule for it

anonymous · Answer

ok. so i should plug in values?

amistre64 · Answer

do you have the derivatives yet?

amistre64 · Answer

once you have the derivatives, determine a suitable value for x that will be able to turn the derivatives into constants

anonymous · Answer

For the derivative i got 2/ (1-x^2)

amistre64 · Answer

youll want a few of them, like for or five if you can to develop a pattern

anonymous · Answer

ohhhhhhh now i see what youre doing. Thanks, i know how to do the problem now. Thanks!

amistre64 · Answer

cool, good luck with the manual labor parts :)

anonymous · Answer

i would divide first

anonymous · Answer

that is, start with 
$$-1+\frac{2}{1-x}$$ then the power series for $\frac{1}{1-x}$ is well known and you can use that one

anonymous · Answer

you get the answer pretty much right away without using a derivative at all 
$$1+2x+2x^2+2x^3+...$$

amistre64 · Answer

well yeah, when you know a few tricks :)

anonymous · Answer

i like tricks