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If The Value Of

$\displaystyle \sum^{\infty}_{n=0}(\dfrac{1}{3n+1}-\dfrac{1}{3n+2})$ = $\gamma$

Then Find $\lfloor10^4 \gamma\rfloor$.

$\textbf{Details}$

$\lfloor \bullet\rfloor$ Is the Greatest Integer Function

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