Let $f(x)=\frac{x+x^{2}+...+x^{n}-n}{x-1},g(x)=(4^{n}+5^{n})^{1/n}$ and $\alpha $ and $\beta $ are the roots of equation $\lim_{x\rightarrow 1}f(x)=\lim_{n\rightarrow \infty }g(x)$, then the value of $\sum_{n=0}^{\infty }(\frac{1}{\alpha }+\frac{1}{\beta })^{n}$ is
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