Tổng \(A=\dfrac{1}{1.5}+\dfrac{1}{5.9}+........+\dfrac{1}{101.105}\) có giá trị là
\(\dfrac{26}{105}\). \(\dfrac{104}{105}\). \(\dfrac{42}{105}\). \(\dfrac{78}{105}\). Hướng dẫn giải:\(A=\dfrac{1}{1.5}+\dfrac{1}{5.9}+........+\dfrac{1}{101.105}\)
\(=\dfrac{1}{4}.\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+........+\dfrac{4}{101.105}\right)\)
\(=\dfrac{1}{4}.\left(\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+.....+\dfrac{1}{101}-\dfrac{1}{105}\right)\)
\(=\dfrac{1}{4}\left(1-\dfrac{1}{105}\right)\)
\(=\dfrac{1}{4}.\dfrac{104}{105}\)
\(=\dfrac{26}{105}\)
