7. Arrange all proper fractions into a sequence $\left\{a_{n}\right\}$ :
$$
\frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \cdots
$$

The sorting method is: from left to right, first arrange the denominators in ascending order, and for fractions with the same denominator, arrange them in ascending order of the numerators. Then $a_{2017}=$ $\qquad$ .
7. $\frac{1}{65}$.

Divide the sequence into segments by the denominator, there are $k$ fractions with the denominator $k+1$, noticing that,
$$
\frac{63 \times 64}{2}=2016, \frac{64 \times 65}{2}=2080,
$$

we know that 2017 belongs to the 64th segment, so $a_{2017}$ should be the first number with the denominator 65, which is $\frac{1}{65}$.