Question

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

Answer 1

分析 因為$\frac{1}{2×4}=\frac{1}{2}×（\frac{1}{2}-\frac{1}{4}）$
$\frac{1}{4×6}=\frac{1}{2}×（\frac{1}{4}-\frac{1}{6}）$
$\frac{1}{6×8}=\frac{1}{2}×（\frac{1}{6}-\frac{1}{8}）$
…
根據(jù)上面的規(guī)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}）$
=$\frac{1}{2}×（\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+…+\frac{1}{16}-\frac{1}{18}+\frac{1}{18}-\frac{1}{20}）$
=$\frac{1}{2}×（\frac{1}{2}-\frac{1}{20}）$
=$\frac{1}{2}×\frac{9}{20}$
=$\frac{9}{40}$

點評 解答此題，應(yīng)注意觀察分?jǐn)?shù)的特點，根據(jù)特點，對分?jǐn)?shù)進(jìn)行拆分，達(dá)到簡算的目的．