# Have you grabbed all the properties of Binomial Coefficients?

Calculus Level 4

Given that $$\displaystyle n = 2\times \sum_{a=1}^\infty \frac{20^a}{(5^a-4^a)(5^{a+1} - 4^{a+1})}$$ and that $$\displaystyle \sum_{r=0}^n (-1)^{r+n} \cdot \frac{ {n\choose r }}{n+r}$$ equals to $$\frac cd$$ for coprime positive integers $$c,d$$, find the value of $$c+d$$.

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