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    (a) Write down the first three terms in the binomial expansion of (1+3x)^n

    (1+3x)^n=1+3xn+(3x^2)\frac{(n(n-1))}{2!}

    I can't do part (b)!!

    (b) By choosing suitable values of n and x, use the series to find \sqrt[3]{1003} to nine significant figures.

    I think that the expansion is valid for |x|<\frac{1}{3} but I'm not sure how it helps me to find the answer to (b)! Any help?
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    (1003)^{1/3}=1000^{1/3}(1+0.003)^{1/3}
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    (Original post by LarsaSolidor)
    (a) Write down the first three terms in the binomial expansion of (1+3x)^n

    (1+3x)^n=1+3xn+(3x^2)\frac{(n(n-1))}{2!}

    I can't do part (b)!!

    (b) By choosing suitable values of n and x, use the series to find \sqrt[3]{1003} to nine significant figures.

    I think that the expansion is valid for |x|<\frac{1}{3} but I'm not sure how it helps me to find the answer to (b)! Any help?
    Choose

    n=\frac{1}{3}

    and let

    1+3x=1003

    Now, what can you do to ensure

    |x| < \frac{1}{3}

    ?
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    (Original post by LarsaSolidor)

    (1+3x)^n=1+3xn+(3x^2)\frac{(n(n-1))}{2!}
    You need (3x)^2 not 3x^2
 
 
 
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