7. Arrange all proper fractions into such 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, for fractions with the same denominator, then arrange them in ascending order of the numerators, then the 2017th term $a_{2017}=$ $\qquad$ .
There are $k$ fractions with the denominator $k+1$. Since $1+2+\cdots+63=\frac{63 \times 64}{2}=2016$, the 2017th term of the sequence is the first number with the denominator 65, so $a_{2017}=\frac{1}{65}$.