1. (10 points) $\frac{1-\frac{1}{3}}{1 \times \frac{1}{2} \times \frac{1}{3}}+\frac{\frac{1}{3}-\frac{1}{5}}{\frac{1}{3} \times \frac{1}{4} \times \frac{1}{5}}+\cdots+\frac{\frac{1}{2015}-\frac{1}{2017}}{\frac{1}{2015} \times \frac{1}{2016} \times \frac{1}{2017}}=$ $\qquad$
【Analysis】Observe that, first, transform the two fractions in the numerator into the product of two fractions, which can exactly cancel out with the denominator, thus simplifying the original complex fraction into simple integer addition and subtraction operations.

【Solution】Solve: $\frac{1-\frac{1}{3}}{1 \times \frac{1}{2} \times \frac{1}{3}}+\frac{\frac{1}{3}-\frac{1}{5}}{\frac{1}{3} \times \frac{1}{4} \times \frac{1}{5}}+\cdots+\frac{\frac{1}{2015}-\frac{1}{2017}}{\frac{1}{2015} \times \frac{1}{2016} \times \frac{1}{2017}}$
$$
\begin{array}{l}
=\frac{\frac{3-1}{1 \times 3}}{1 \times \frac{1}{2} \times \frac{1}{3}}+\frac{\frac{5-3}{3 \times 5}}{\frac{1}{3} \times \frac{1}{4} \times \frac{1}{5}}+\cdots+\frac{\frac{2017-2015}{2015 \times 2017}}{\frac{1}{2015} \times \frac{1}{2016} \times \frac{1}{2017}} \\
=\frac{2 \times \frac{1}{1 \times 3}}{\frac{1}{1 \times 3} \times \frac{1}{2}}+\frac{2 \times \frac{1}{3 \times 5}}{\frac{1}{3 \times 5} \times \frac{1}{4}}+\frac{2 \times \frac{1}{5 \times 7}}{\frac{1}{5 \times 7} \times \frac{1}{6}}+\cdots+\frac{2 \times \frac{1}{2015 \times 2017}}{\frac{1}{2015 \times 2017} \times \frac{1}{2016}} \\
=2 \times(2+4+6+8+\cdots+2016) \\
=2 \times \frac{(2+2016)}{2} \times \frac{2016}{2} \\
=2018 \times 1008 \\
=2034144 \\
\end{array}
$$