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Math Help - Calculating terms of the Maclaurin series for a function

  1. #1
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    Calculating terms of the Maclaurin series for a function

    Hi guys, i've got this exercise which requires me to calculate the first three terms of the Maclaurin seris for the sqr root of (1 + x)

    My attempt gives me ( i don't know the code for the sqr root symbol so i've left it out but there should be the sqr root symbol on every term of the series:

     f(1 + x) = f(1 + 0) + f'(1 + 0)(x) \, /2 + f'1(1 + 0)(x^2) +...

    If anything is wrong i would greatly appreciate it, if you point out and feel free to make corrections.

    Thanks a bunch.
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  2. #2
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    The first term is just 1.

    \frac{d}{dx}[\sqrt{1+x}]=\frac{1}{2\sqrt{x+1}}

    \frac{d^{2}}{d^{2}x}[\sqrt{1+x}]=\frac{-1}{4(x+1)^{\frac{3}{2}}}

    Now, if we use them in the MacLauren series and let x=0:

    1+\frac{x}{2}-\frac{x^{2}}{8}+..........
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