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Math Help - geometric power series

  1. #1
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    geometric power series

    My questions require me to put functions into the a/(1-r) form. I don't understand how to do this.

    The question- Find a power series for the function, centered at c, and determine the interval of convergence.

    f(x)= 1/(2-x), c=5

    How do I put this into the a/(1-r) form?
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  2. #2
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    Quote Originally Posted by jlmills5 View Post
    My questions require me to put functions into the a/(1-r) form. I don't understand how to do this.

    The question- Find a power series for the function, centered at c, and determine the interval of convergence.

    f(x)= 1/(2-x), c=5

    How do I put this into the a/(1-r) form?
    Divide both numerator and denominator by 2!
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  3. #3
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    I can see that, but what about the c=5? I don't understand how to incorporate that and create the a/(1-r) form.

    My key shows 1/(-3-(x-5)) = (-1/3)/(1+(1/3)(x-5))

    I can see how they derived the 2nd part from the first, but I have no clue how they even got the first part! Help!
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  4. #4
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    If you want a series centered at c = 0, you let r be something times x. If you want a series centered at c = 5, you let r be something times x-5. To get an x-5 in the denominator, you do the following:
     2 - x = 2 - x + 5 - 5 \\<br />
= -3 - x + 5 \\<br />
= -3 - (x-5) .
    Then proceed to divide the numerator and denominator by -3. Then you'll have the appropriate form with a = -1/3 and r = (1/3)(x-5).
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  5. #5
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    Thank you, thank you, thank you!
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