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Math Help - First 25 digits after decimal point of (sqrt(10)+5)^100?

  1. #1
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    Dec 2010
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    First 25 digits after decimal point of (sqrt(10)+5)^100?

    How would you go about finding the first 25 digits after decimal point of (\sqrt{10}+5)^{100}? (without using calculator)
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  2. #2
    Senior Member
    Joined
    Mar 2010
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    To begin with

    <br />
(1+x)^{1/2}=1+\frac{1}{2}x-\frac{1}{8}x^2+...<br />

    <br />
(1+9)^{1/2}=3(1+\frac{1}{9})^{1/2}=...<br />

    You must evaluate number of terms needed for this accuracy.

    The same with

    <br />
(1+x)^{100}=...<br />
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