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Math Help - Representations of Functions as Power series

  1. #1
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    Question Representations of Functions as Power series

    Find the first cofefficients

    f(x)=7/(1+64x^2)= summation n=0 to infinity (c_n)(x^n)
    c_1
    c_2
    c_3
    c_4

    I really don't know how to do this. I know you could right it as summation n=0 to infinity 7*(-1)^n (64x^2)^n i'm not even sure that it is even right. please help
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  2. #2
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    Quote Originally Posted by will_lansing View Post
    Find the first cofefficients

    f(x)=7/(1+64x^2)= summation n=0 to infinity (c_n)(x^n)
    c_1
    c_2
    c_3
    c_4

    I really don't know how to do this. I know you could right it as summation n=0 to infinity 7*(-1)^n (64x^2)^n i'm not even sure that it is even right. please help

    Use either the binomial theorem, or McLaurin/Taylor series.

    RonL
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    what is the binomial theorem, or McLaurin/Taylor series
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  4. #4
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    Quote Originally Posted by will_lansing View Post
    what is the binomial theorem, or McLaurin/Taylor series
    What have you covered so far in your course? Also, what course is it?

    see here for binomial theorem

    and here for Taylor/Mclaurin series

    RonL
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  5. #5
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    I'm in Calc 2 and we just covered differentiation and integration of power series. so which of the two method is the best to use for this problem
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by will_lansing View Post
    I'm in Calc 2 and we just covered differentiation and integration of power series. so which of the two method is the best to use for this problem
    I would use the binomial expansion, because I can just write it down without
    computing derivatives.

    RonL
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