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Math Help - Convergence in the form p^n/n!

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    Convergence in the form p^n/n!



    Are these sufficient answers? I feel like maybe they are not convincing enough...
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by davismj View Post


    Are these sufficient answers? I feel like maybe they are not convincing enough...
    They don't convince me at all. Can you explain your reasoning?
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    Quote Originally Posted by Drexel28 View Post
    They don't convince me at all. Can you explain your reasoning?
    well, any complex number z can be written \rho(e^i\theta), and \rho \in R : \rho = |z|.

    Therefore \sum\rho^n/n! = e^\rho.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by davismj View Post
    well, any complex number z can be written \rho(e^i\theta), and \rho \in R : \rho = |z|.

    Therefore \sum\rho^n/n! = e^\rho.
    Yes, but \lim\text{ }a_n=0\implies \sum_{n=1}^{\infty}a_n<\infty?
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    Quote Originally Posted by Drexel28 View Post
    Yes, but \lim\text{ }a_n=0\implies \sum_{n=1}^{\infty}a_n<\infty?
    No, although in this case we know that since \rho is real, the sum is actually equal to e^\rho. Should I write that down?

    Thank you for your help!
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by davismj View Post
    No, although in this case we know that since \rho is real, the sum is actually equal to e^\rho. Should I write that down?

    Thank you for your help!
    That isn't how to do this. Try using the ratio test.
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    Quote Originally Posted by Drexel28 View Post
    That isn't how to do this. Try using the ratio test.
    I see now. I was making things harder than necessary.
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