Good Day,

I've been faced with a funny binomial expansion. Attached it with the answer from the book for your reference.

My question is, how do we get to the answer if I expanded (1-2x)^-2 first and then multiplied it with cos x?

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- Dec 13th 2010, 08:36 AMdd86Binomial Expansion
Good Day,

I've been faced with a funny binomial expansion. Attached it with the answer from the book for your reference.

My question is, how do we get to the answer if I expanded (1-2x)^-2 first and then multiplied it with cos x? - Dec 13th 2010, 09:12 AMFernandoRevilla
Yes,

Fernando Revilla - Dec 13th 2010, 09:37 AMchisigma
Your approach is fully correct!... the series expansion of the term is obtained with the following steps...

(1)

http://digilander.libero.it/luposaba...ato[1].jpg

Merry Christmas from Italy

- Dec 13th 2010, 05:02 PMdd86
Wow OK. I did not come across this in my self-study so far...

So what this means is that when I multiply a binomial expansion with cos x, I have to differentiate the binomial expansion?

What if it was cos 2x or cos3x or cos -x? Do I differentiate that many times for positive integers and integrate that many times for negative ones? What if it was cos ax if a is not an integer?

What about sin ax and tan ax?

It would be great if anyone could just give me the link to read up on this. I'm still a novice so something that's easy to understand would be preferable. But I will post questions if I don't understand :p - Dec 13th 2010, 05:19 PMdd86
I'd also like to know whether I can read up on how to find the rth term in a binomial expansion? I have found myself to be weak in this part for many of the questions I have come across.

Is this covered in a different topic in math?

Will post a sample question about this soon. - Dec 13th 2010, 06:23 PMTheCoffeeMachine
The series expansion of can also be found this way:

@ dd86:

__Spoiler__: - Dec 17th 2010, 11:26 PMdd86
Thank you, The CoffeMachine. Your tip with finding the rth term was very helpful. Had alotta fun in solving the questions I had left out before.

- Dec 18th 2010, 04:27 AMHallsofIvy
No, he didn't say that. Chisigma did not use the binomial expansion, he used the derivatives to find the Taylor's series for . Of course, "a power series is a power series" so both methods give the same result.

Quote:

What if it was cos 2x or cos3x or cos -x? Do I differentiate that many times for positive integers and integrate that many times for negative ones? What if it was cos ax if a is not an integer?

What about sin ax and tan ax?

It would be great if anyone could just give me the link to read up on this. I'm still a novice so something that's easy to understand would be preferable. But I will post questions if I don't understand :p