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HELP !! C2 QUESTION ON SERIES AND SEQUENCES - binomial expansion watch

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    HEY :P
    a )Expand (1 + 2X)^10 in ascending powers of x up to and including the term in x^3
    , simplifying
    each coefficient.

    ANSWER : 1 + 5x + (45/4X)^2 + 15X^3 +....

    b) By substituting a suitable value of x into your answer for part a, obtain an estimate for
    i 1.00510 ii 0.99610
    giving your answers to 5 decimal places.

    I'm confused as to how to solve part b are we to just guess and use trial and error which number would give a close enough number to what they are asking for ,or is there a way to actually solve it ?

    thank you , would appreciate the help
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    I think you do 1 + 2X = 1.0051 and solve for X, then substitute that value into your expansion for an approximation (so X would be 0.00255 in this case)
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    (Original post by Sadilla)
    HEY :P
    a )Expand (1 + 2X)^10 in ascending powers of x up to and including the term in x^3
    , simplifying
    each coefficient.

    ANSWER : 1 + 5x + (45/4X)^2 + 15X^3 +....

    b) By substituting a suitable value of x into your answer for part a, obtain an estimate for
    i 1.00510 ii 0.99610
    giving your answers to 5 decimal places.

    I'm confused as to how to solve part b are we to just guess and use trial and error which number would give a close enough number to what they are asking for ,or is there a way to actually solve it ?

    thank you , would appreciate the help
    Your expansion is valid for |2x| < 1 therefore we must get |x| < \frac{1}{2}.

    If we wish to approximate 1.005^{10} then we can say 1+2x = 1.005 and hence x=0.0025 which is indeed in our range.

    So we can just sub that into the expansion.
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    (Original post by RDKGames)
    Your expansion is valid for |2x| < 1 therefore we must get |x| < \frac{1}{2}.

    If we wish to approximate 1.005^{10} then we can say 1+2x = 1.005 and hence x=0.0025 which is indeed in our range.

    So we can just sub that into the expansion.
    thank you so much
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    (Original post by MathsPhysMind)
    I think you do 1 + 2X = 1.0051 and solve for X, then substitute that value into your expansion for an approximation (so X would be 0.00255 in this case)
    thank you
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    (Original post by Sadilla)
    HEY :P
    a )Expand (1 + 2X)^10 in ascending powers of x up to and including the term in x^3
    , simplifying
    each coefficient.

    ANSWER : 1 + 5x + (45/4X)^2 + 15X^3 +....
    This is an expansion of (1 + x/2)^10 rather than of (1 + 2x)^10.
 
 
 
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