# Nested Square Root Sum (And Triangular Numbers)

Algebra Level 5

The value of $\sum_{k=1}^{2015} \sqrt{\sqrt{T_k+\dfrac{1}{8}}-\sqrt{T_k}}$ where $$T_k$$ is the $$k$$th triangular number, can be expressed as $\sqrt{\sqrt{\dfrac{p}{q}}-\sqrt{r}}$ for positive integers $$p,q,r$$ and $$\gcd(p,q) = 1$$. Find the last three digits of $$p+q+r$$.

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