Calculus III : Getting MacLaurin Series From Functions

[K3nt70]

Homework Statement

5) For each of the series below, write the series in summation notation and give the first five terms of the series. Also give the radius of convergence of the series.

a) Use the series for $$\frac{1}{1 - x}$$ to find the Maclaurin series of

$$f(x) = \frac{1}{(1-2x)^3}$$

Homework Equations

R = 1/L

The Attempt at a Solution

I have the full solution set for this problem but i can't figure out the process they are using to obtain the answer. I'm pretty unclear on specifically what the answer is supposed to be. I see that i am supposed to write the series in summation notation, but i don't know all of the steps.

For some reason they begin taking derivatives of the series given in the question and i have no idea why. All i really need help with is how to approach the problem. A little insight on what I'm supposed to be doing here would be great.

Thanks,

-Kent

 

[Dick]

If you know the series for 1/(1-x)=1+x+x^2+x^3+... then if you take the derivatives of both sides you get 1/(1-x)^2=1+2x+3x^2+4x^3+... Et voila. There's series for 1/(1-x)^2. I think that's the general outline of what they are doing. Does that help?

 

[K3nt70]

That's def. enough to get me started - i'll see where it gets me.


thanks