What is the value of $999 \frac{1}{2}+999 \frac{1}{6}+999 \frac{1}{12}+$ $999 \frac{1}{20}+999 \frac{1}{30} ?$

Expression

$=999 \frac{1}{2}+999 \frac{1}{6}+999 \frac{1}{12}+999 \frac{1}{20}+999 \frac{1}{30}$

$=5 \times 999+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)$

$=4995+\left(\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\frac{1}{4 \times 5}+\frac{1}{5 \times 6}\right)$

$=4995+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\right.$

$\left.\frac{1}{5}-\frac{1}{6}\right)$

$=4995+\left(1-\frac{1}{6}\right)=4995+\frac{5}{6}=4995 \frac{5}{6}$