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 \(x+y+z.\)
by
Anastasiya Romanova
