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    (1 + 2x)^(1/2) x ( 1 + x )^3

    State the set of value of x for which the expansion os valid.

    Which bracket do you use?
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    (Original post by IShouldBeRevising_)
    (1 + 2x)^(1/2) x ( 1 + x )^3

    State the set of value of x for which the expansion os valid.

    Which bracket do you use?
    Hint:

    (1+x)^3 = x^3 + 3x^2 + 3x + 1

    works for all x.
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    (Original post by IShouldBeRevising_)
    (1 + 2x)^(1/2) x ( 1 + x )^3

    State the set of value of x for which the expansion os valid.

    Which bracket do you use?
    Whichever imposes the greater restriction.
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    (Original post by Indeterminate)
    Hint:

    (1+x)^3 = x^3 + 3x^2 + 3x + 1

    works for all x.

    (Original post by joostan)
    Whichever imposes the greater restriction.
    So the one with the smallest power?
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    (Original post by IShouldBeRevising_)
    So the one with the smallest power?
    In this case yes, but not generally.
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    (Original post by joostan)
    In this case yes, but not generally.
    What do you mean by imposea thw greatest reatriction?
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    (Original post by IShouldBeRevising_)
    What do you mean by imposea thw greatest reatriction?
    the one which stops the binomial increasing further, basically if you bionomial expand (1+x) you will only get 1+x, where as (1+x)^3 can expand further so you take the restriction of the first one because its has the smallest range of value possible.
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    (Original post by IShouldBeRevising_)
    (1 + 2x)^(1/2) x ( 1 + x )^3

    State the set of value of x for which the expansion os valid.

    Which bracket do you use?
    Haha these answers are all unnecessarily complicated and irrelevant , I doubt they've helped you at all

    The answer you're looking for is: the one with the smaller range
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    (Original post by IShouldBeRevising_)
    What do you mean by imposea thw greatest reatriction?
    What is the requirement for mod(x) for the binomial expansion of (1+x)n where n is not a positvie integer (or 0)?
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    (Original post by Rump Steak)
    Haha these answers are all unnecessarily complicated and irrelevant , I doubt they've helped you at all

    The answer you're looking for is: the one with the smaller range
    What do you mean by smallest range?
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    (Original post by IShouldBeRevising_)
    What do you mean by smallest range?
    Do you know how to find out the range of x for which a bracket is valid??
    If you do, find out what it is for the first bracket, then find it out for the second one, and whichever range is smallest is the one valid for the whole equation.
    If you don't... Well you should, have a read of your notes I guess
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    (Original post by yaboy)
    the one which stops the binomial increasing further, basically if you bionomial expand (1+x) you will only get 1+x, where as (1+x)^3 can expand further so you take the restriction of the first one because its has the smallest range of value possible.
    No, because both those expansions are finite so there is no restriction on x.

    The thing that matters is when one of the expansions is an infinite series, in which case it has a restricted range of validity.
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    (Original post by Rump Steak)
    Do you know how to find out the range of x for which a bracket is valid??
    If you do, find out what it is for the first bracket, then find it out for the second one, and whichever range is smallest is the one valid for the whole equation.
    If you don't... Well you should, have a read of your notes I guess
    Yes I do thanks I get it now
 
 
 
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