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Math Help - integral, power series

  1. #1
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    integral, power series

    I've never been very good at integrals, i need help with this one please.

    Evaluate the indefinite integral as a power series. What is the radius of convergence?

    INT t/(1 - t^4) dt

    thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    I've never been very good at integrals, i need help with this one please.

    Evaluate the indefinite integral as a power series. What is the radius of convergence?

    INT t/(1 - t^4) dt

    thanks.

    INT t/(1 - t^4) dt = integral t + t^5 + t^9 + .. + t^{4n-3} + ... dt

    .........................= t^2/2 + t^6/2 + ... + t^{4n-2)}/(4n-2) + ..

    ........................= Sum_{n=1, infty} t^{4n-2)}/(4n-2)

    and its radius of convergence should be |t|<1.

    RonL
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