`A = 5/(1*3) + 5/(3*5) + …. + 5/(99*101)` Tính. 11/08/2021 Bởi Iris `A = 5/(1*3) + 5/(3*5) + …. + 5/(99*101)` Tính.
`A = 5/{1.3} + 5/{3.5} + … + 5/{99.101}` `A = 5/2 . 2/{1.3} + 5/2 . 2/{3.5} + … + 5/2 . 2/{99.101}` `A = 5/2(2/{1.3} + 2/{3.5} + … + 2/{99.101} )` `A = 5/2 (1 – 1/3 + 1/3 – 1/5 + … + 1/99 – 1/101 )` `A = 5/2 ( 1 – 1/101)` `A = 5/2 . 100/101` `A = 250/101` Bình luận
A=$\frac{5}{1.3}$+$\frac{5}{3.5}$+…+$\frac{5}{99.101}$ =$\frac{5}{2}$ .($\frac{2}{1.3}$+$\frac{2}{3.5}$+…+$\frac{2}{99.101}$ ) =$\frac{5}{2}$ .($1-\frac{1}{3}$+$\frac{1}{3}$-$\frac{1}{5}$+…+$\frac{1}{99}$-$\frac{1}{101}$ ) =$\frac{5}{2}$ .($1-\frac{1}{101}$) =$\frac{5}{2}$ .\frac{100}{101}$ =$\frac{250}{101}$ Bình luận
`A = 5/{1.3} + 5/{3.5} + … + 5/{99.101}`
`A = 5/2 . 2/{1.3} + 5/2 . 2/{3.5} + … + 5/2 . 2/{99.101}`
`A = 5/2(2/{1.3} + 2/{3.5} + … + 2/{99.101} )`
`A = 5/2 (1 – 1/3 + 1/3 – 1/5 + … + 1/99 – 1/101 )`
`A = 5/2 ( 1 – 1/101)`
`A = 5/2 . 100/101`
`A = 250/101`
A=$\frac{5}{1.3}$+$\frac{5}{3.5}$+…+$\frac{5}{99.101}$
=$\frac{5}{2}$ .($\frac{2}{1.3}$+$\frac{2}{3.5}$+…+$\frac{2}{99.101}$ )
=$\frac{5}{2}$ .($1-\frac{1}{3}$+$\frac{1}{3}$-$\frac{1}{5}$+…+$\frac{1}{99}$-$\frac{1}{101}$ )
=$\frac{5}{2}$ .($1-\frac{1}{101}$)
=$\frac{5}{2}$ .\frac{100}{101}$
=$\frac{250}{101}$