# $$nx^2-x+n(n+1)=0$$

Algebra Level 3

For all positive integers $$n$$, let $$\alpha_n$$ and $$\beta_n$$ be the roots of the quadratic equation $nx^2-x+n(n+1)=0.$ What is the value of $\left(\frac{1}{\alpha_1}+\frac{1}{\beta_1}\right)+\left(\frac{1}{\alpha_2}+\frac{1}{\beta_2}\right)+ \cdots +\left(\frac{1}{\alpha_{25}}+\frac{1}{\beta_{25}}\right)?$

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