# Reciprocal sum of roots

Level pending

For $$i=1,2...,2014$$ let $$\alpha_i$$ and $$\beta_i$$ be the roots of

$$x^2-2x-i^2-i=0$$.

The value of

$$\displaystyle\sum_{i=1}^{2014}\frac{1}{\alpha_i}+\frac{1}{\beta_i}$$

can be expressed as $$-\frac{a}{b}$$, where a and b are coprime positive integers.What is the value of b-2014?

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