Ta có:\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+......+\frac{1}{81.85}\)
\(=\frac{1}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+......+\frac{4}{81.85}\right)\)
\(=\frac{1}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+.......+\frac{1}{81}-\frac{1}{85}\right)\)
\(=\frac{1}{4}.\left(1-\frac{1}{85}\right)\)
\(=\frac{1}{4}.\frac{84}{85}=\frac{21}{85}\)
\(A=\frac{1}{1.5}+\frac{1}{5.9}+...+\frac{1}{81.85}\)
Ta có công thức
\(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)
\(\Rightarrow A=\frac{1}{4}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+..+\frac{1}{81}-\frac{1}{85}\right)\)
\(A=\frac{1}{4}.\left(1-\frac{1}{85}\right)\)
\(A=\frac{84}{340}\)
