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Thread: Binomial series

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    Binomial series

    I'm completely stuck on the question, Find the square root of 51 correct to 4dp using binomail series. Ive attempted this but clearly made a serious error somewhere because the numbers get very large indeed.
    Any help would be great
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  2. #2
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    Quote Originally Posted by verlindenl View Post
    Find the square root of 51 correct to 4dp using binomial series.
    \sqrt{51} = \sqrt{49+2} = 7\sqrt{1+(2/49)}. Use the binomial expansion of (1+x)^{1/2} with x = 2/49. The terms will get small quite rapidly, so you should not need very many to get within 4dp accuracy. (Don't forget to multiply by 7 at the end to get the correct answer.)
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