36. Given $\frac{x}{1 \times 2}+\frac{x}{2 \times 3}+\frac{x}{3 \times 4}+\ldots+\frac{x}{999 \times 1000}=999$. Then $x=$
Answer: 1000.
Solution: The equation given in the problem is
$$
\begin{array}{c}
x\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\ldots+\frac{1}{999}-\frac{1}{1000}\right)=999, \\
x\left(1-\frac{1}{1000}\right)=999,
\end{array}
$$

Solving for \( x \) yields
$$
x=1000 \text {. }
$$