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Let f(x)=(x+x^2+...+x^n-n)/(x-1), g(x)=(...

Let `f(x)=(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 rarr 1) f(x)= lim_(n rarr oo) g(x)` then the value of `sum_(n=0)^oo (1/alpha+1/beta)^n` is

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