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Problem of the Day #126: Annoying Sums July 23, 2011

Posted by Albert in : potd , trackback

Arjun is locked in jail with paper and a pencil and is told he will be freed if and only if he correctly evaluates the following problem: $$\sum\limits_{k=8}^{\infty} \frac{1}{k(k^2-6k+8)}$$
You are allowed to give him one hint, so once you’ve realized the result is obviously a fraction, you choose to tell him what the sum of the numerator and denominator is…

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