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Thread: Mathematical Induction - Unknown general term for the sum side.

  1. #1
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    Mathematical Induction - Unknown general term for the sum side.

    I cannot find the general term for the sum for this sequence. Been doing it for hours and I cannot proceed with induction without it. Help would be greatly appreciated. Please view the photo URL: https://imgur.com/pXHvSoa
    Last edited by Bumdwarf; Mar 13th 2018 at 09:11 AM.
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  2. #2
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    Re: Mathematical Induction - Unknown general term for the sum side.

    Quote Originally Posted by Bumdwarf View Post
    I cannot find the general term for the sum for this sequence. Been doing it for hours and I cannot proceed with induction without it. Help would be greatly appreciated. Please view the photo URL: https://imgur.com/pXHvSoa
    Try plugging it into Wolframalpha. It says that the sum is extremely messy:

    Wolfram|Alpha: Computational Knowledge Engine

    The sum uses the digamma function. Keep in mind the recurrence relation that $\psi(x+1) = \psi(x) + \dfrac{1}{x}$
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