Not A Telescoping Sum

Calculus Level 5

k=1(13k113k)\large \sum_{k = 1}^{\infty} \left(\dfrac{1}{3k-1}-\dfrac{1}{3k}\right)

The above sum has a closed form of lnABπCD2E  \large \dfrac{\ln{A}}{B} - \dfrac{\pi\sqrt{C}}{D^2 E} \; where A,B,C,DA,B,C,D and EE are positive prime numbers. Find the value of A+B+C+D+EA+B+C+D+E.

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