Question 17
For each natural number $n$, let $a_n$ be the greatest perfect square number lower than or equal to $n$ and $b_n$ the smallest perfect square number greater than $n$. For instance, $a_9 = 3^2$, $b_9 = 4^2$, $a_{20} = 4^2$ and $b_{20} = 5^2$.
Calculate the sum of the 600 terms
$$
\frac{1}{a_1b_1} + \frac{1}{a_2b_2} + \dots + \frac{1}{a_{600}b_{600}}
$$
Calculate the sum of the 600 terms
$$
\frac{1}{a_1b_1} + \frac{1}{a_2b_2} + \dots + \frac{1}{a_{600}b_{600}}
$$