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# P3 Question: (Medium Difficulty) watch

1. You are given a fraction which is simplified to: -2x(1+x^2)^(-1) or if you like -2x/(1+x^2)
Then you have to expand this in ascending powers of x up to x^3 inclusive.

I am having problems trying to convert the equation into a form that will give me (1+mx)^n or k(1+mx)^n, which I can then expand.

I'm not sure if it's actually possible? If it is possible please provide yer full method

Thank You. Bye
2. (Original post by ResidentEvil)
-2x(1+x^2)^(-1)
-2x(1 - x^2 + [(-1)(-2)(x^2)^2]/2! + [(-1)(-2)(-3))(x^2)^3]/3!)

If you follow the above through then you sould find that the expansion only produces a term in x and a term in x^2.

I think its 2x^3 - 2x

PS - Dont blame me if it is wrong....havent revised expansions yet.
3. (Original post by ResidentEvil)
You are given a fraction which is simplified to: -2x(1+x^2)^(-1) or if you like -2x/(1+x^2)
Then you have to expand this in ascending powers of x up to x^3 inclusive.

I am having problems trying to convert the equation into a form that will give me (1+mx)^n or k(1+mx)^n, which I can then expand.

I'm not sure if it's actually possible? If it is possible please provide yer full method

Thank You. Bye
you can expand it normally...the x^2 doesn't bug the equation.

I get -2x(1+x^2)^-1= -2x(1 - x^2 +...)
= -2x + x^3 +.....

does this help?
4. (Original post by p8224)
you can expand it normally...the x^2 doesn't bug the equation.

I get -2x(1+x^2)^-1= -2x(1 - x^2 +...)
= -2x + x^3 +.....

does this help?
nah, thats incorrect, i tried that. It looks incorrect anyway, coz the theory is, u can expand (1+nx)^m but not anything in a different form.
5. (Original post by p8224)
you can expand it normally...the x^2 doesn't bug the equation.

I get -2x(1+x^2)^-1= -2x(1 - x^2 +...)
= -2x + x^3 +.....

does this help?
You just have to remember that X^2 is the same as XX when in the form mx. also make sure you multiple your indicies when you expand.

MB
6. (Original post by ResidentEvil)
nah, thats incorrect, i tried that. It looks incorrect anyway, coz the theory is, u can expand (1+nx)^m but not anything in a different form.
hmmm....what is the answer? maybe we could try working backwords...
7. (Original post by musicboy)
You just have to remember that X^2 is the same as XX when in the form mx. also make sure you multiple your indicies when you expand.

MB
Are you allowed to do that? m is a constant and x is a variable, so I would never have even thought to do that.
8. OK TO END ALL OF YOU GUYS MISERY:
(Original post by mikesgt2)
Firstly, consider the bracket (1+x^2)^(-1). You can show that

(1+y)^(-1) = 1 - y + y^2 - y^3 + ...

So, if we let y=x^2 we see that

(1+x^2)^(-1) = 1 - x^2 + x^4 - x^6 + ...

Multiplying by -2x gives

-2x(1+x^2)^(-1) = -2x + 2x^3 - 2x^5 + 2x^7 - ...

which I think this is the answer. I hope this helps.
Many thanks to Mike! I have seen this 'style' of question before but couldnt remember how to do it, and now its rehearsed my memory, and i remember that is how its done - thanks mike once again.
9. (Original post by ResidentEvil)
OK TO END ALL OF YOU GUYS MISERY:
hahahah!

that's what i did!...except i forgot to muliply by 2 when i expanded my answer....and i didnt bother with the x^5 term...
10. (Original post by ResidentEvil)
nah, thats incorrect, i tried that. It looks incorrect anyway, coz the theory is, u can expand (1+nx)^m but not anything in a different form.
I'm quite sure that in the expansion of (1 + mx)^n....m can be a scalar or any function of x....the only requirement for using this expansion is that it must be 1 at the start
11. (Original post by ResidentEvil)
You are given a fraction which is simplified to: -2x(1+x^2)^(-1) or if you like -2x/(1+x^2)
Then you have to expand this in ascending powers of x up to x^3 inclusive.

I am having problems trying to convert the equation into a form that will give me (1+mx)^n or k(1+mx)^n, which I can then expand.

I'm not sure if it's actually possible? If it is possible please provide yer full method

Thank You. Bye
which board is this for?edexcel?
12. (Original post by Tanaz)
which board is this for?edexcel?
It's on the eddexcel syllabus. Chapter 1 from P3 or Sequences and series chapter from P2.

MB
13. write y = x²

the denominator is (1+y)^(-1), and you can expand this normally

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