# The Easy Peasy Double Sum of Series

Calculus Level 5

The value of the following double sum of series

$\sum_{\large m=0}^{\large\infty}\sum_{\large n=0}^{\large2014}\binom{m}{n}\left(\frac{2}{3}\right)^{\large m+1}$

can be expressed as $$\displaystyle{\frac{2^{\large x}-2^{\large y}}{3^{\large z}}}.$$ Find $$x+y+z.$$

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