Can it be summed up?

Algebra Level 4

$\large \sum_{n = 1}^{9800} \dfrac{1}{\sqrt{n + \sqrt{n^2 - 1}}}$

If the sum above can be expressed as $$p + q \sqrt{r}$$, where $$p, q$$ and $$r$$ are positive integers and $$r$$ is not divisible by the square of any prime, determine $$p + q + r$$.

×