If , find the value of…

MATHEMATICS · Numerical · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

If k=∑n=1∞6n(3n−2n)(3n+1−2n+1)k=\sum_{n=1}^{\infty}\frac{6^n}{(3^n-2^n)(3^{n+1}-2^{n+1})}, find the value of kk.

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