Question

5．计算：$\frac{1}{2×4}+\frac{1}{4×6}+\frac{1}{6×8}+…+\frac{1}{16×18}+\frac{1}{18×20}$．

Answer 1

分析 因为$\frac{1}{2×4}=\frac{1}{2}×（\frac{1}{2}-\frac{1}{4}）$
$\frac{1}{4×6}=\frac{1}{2}×（\frac{1}{4}-\frac{1}{6}）$
$\frac{1}{6×8}=\frac{1}{2}×（\frac{1}{6}-\frac{1}{8}）$
…
根据上面的规律解答．

解答 解：$\frac{1}{2×4}+\frac{1}{4×6}+\frac{1}{6×8}+…+\frac{1}{16×18}+\frac{1}{18×20}$
=$\frac{1}{2}×（\frac{1}{2}-\frac{1}{4}）+\frac{1}{2}×（\frac{1}{4}-\frac{1}{6}）+\frac{1}{2}×（\frac{1}{6}-\frac{1}{8}）+…+$$\frac{1}{2}×（\frac{1}{16}-\frac{1}{18}）+\frac{1}{2}×（\frac{1}{18}-\frac{1}{20}）$
=$\frac{1}{2}×（\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+…+\frac{1}{16}-\frac{1}{18}+\frac{1}{18}-\frac{1}{20}）$
=$\frac{1}{2}×（\frac{1}{2}-\frac{1}{20}）$
=$\frac{1}{2}×\frac{9}{20}$
=$\frac{9}{40}$

点评 解答此题，应注意观察分数的特点，根据特点，对分数进行拆分，达到简算的目的．