\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}+\frac{1}{6\times 7}= ．
\frac{1}{2}
\frac{1}{7}
\frac{2}{7}
\frac{5}{14}
\frac{9}{14}
=\left( \frac{1}{2}-\frac{1}{3} \right)+\left( \frac{1}{3}-\frac{1}{4} \right)+\left( \frac{1}{4}-\frac{1}{5} \right)+\left( \frac{1}{5}-\frac{1}{6} \right)+\left( \frac{1}{6}-\frac{1}{7} \right)
=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}
=\frac{1}{2}-\frac{1}{7}
=\frac{5}{14}．
