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Math Help - Problem understanding power series and radius of convergence....please help

  1. #1
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    Problem understanding power series and radius of convergence....please help

    I must be really stupid because everyone says these are really easy but I just don't get it. Even the tutor at the math lab said he couldn't help because I didn't get it.

    So, anyways....

    The problem is "suppose that 2x/(3+x)= sum cn x^n from n=0 to inf
    Find the first few coefficients and R

    I found c0 by just replacing n with 0 which gets 0.
    I found c1 on accident 2/3

    I don't know how to find R or c2,c3,c4

    I thought this was the same as sum ax^n with a being 2x/(3+x) but I must be wrong.

    I swear this is the last time I am taking a math class online with no help from the professor....
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  2. #2
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    Quote Originally Posted by operaphantom2003 View Post
    I must be really stupid because everyone says these are really easy but I just don't get it. Even the tutor at the math lab said he couldn't help because I didn't get it.

    So, anyways....

    The problem is "suppose that 2x/(3+x)= sum cn x^n from n=0 to inf
    Find the first few coefficients and R

    I found c0 by just replacing n with 0 which gets 0.
    I found c1 on accident 2/3

    I don't know how to find R or c2,c3,c4

    I thought this was the same as sum ax^n with a being 2x/(3+x) but I must be wrong.

    I swear this is the last time I am taking a math class online with no help from the professor....

    Put f(x):=\frac{2x}{x+3}=\sum^\infty_{n=1}c_nx^n and differentiate on one hand the rational function and on the other hand the power series, and then compare each when taking x=0 ...

    Tonio
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