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    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
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    (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.
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    (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?
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    (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.
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    (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
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    (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...
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    (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.
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    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.
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    (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...
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    (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
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    (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?
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    (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
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    write y = x²

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