Question 44
Define $f(r) = 2\sqrt{r} + \sqrt{r-1} + \sqrt{r+1}$, $g(r) = 2\sqrt{r} + \sqrt{r-1} - \sqrt{r+1}$ and $h(r) = 2\sqrt{r} - \sqrt{r-1} + \sqrt{r+1}$. Calculate to two decimal places
$$
\sum_{r=1}^{2020} \frac{1}{f(r) \cdot g(r) \cdot h(r)}.
$$
$$
\sum_{r=1}^{2020} \frac{1}{f(r) \cdot g(r) \cdot h(r)}.
$$