I Don't Think the a Should be There

Calculus Level 5

\[\displaystyle \sum_{x=1}^{\infty} \displaystyle \log_{33}\left(\frac{(x+a-1)(x+a+1)}{(x+a-3)(x+a+3)}\right)=1\]

If the sum of all possible real values of constant \(a\) such that the infinite sum above is fulfilled can be represented as \(\frac{p}{q}\) for coprime positive integers \(p,q\), find \(p+q\).

Try the harder (way harder) version here.

Try the easier version here.


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