Toán Tính A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + …………. + 1/ 98.99.100 17/07/2021 By Emery Tính A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + …………. + 1/ 98.99.100
Đáp án: `4949/19800` Giải thích các bước giải: `A` `=` `1/1` `.` `2.3` `+` `1/2` `.` `3` `.` `4` `+` `1/3` `.` `4` `.` `5` `+` `…` `+` `1/ 98.99.100` `=` `1/2` `-` `1/2.3` `+` `1/2.3` `-` `1/3.4` `+` …. `1/98.99` `-` `1/99.100` `=` `1/1.2` `-` `1/99.100` `=` `4949/19800` $#Đào$ Trả lời
`A = 1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))` `A = 1/2 . 2 . (1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))` `A = 1/2 . (2 . 1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))` `A = 1/2 . (2/(1 . 2 . 3) + 2/(2 . 3 . 4) + 2/(3 . 4 . 5) + … + 2/(98 . 99 . 100))` `A = 1/2 . (1/(1 . 2) – 1/(2 . 3) + 1/(2 . 3) – 1/(3 . 4) + … + 1/(98 . 99) – 1/(99 . 100))` `A = 1/2 . (1/(1 . 2) – 1/(99 . 100))` `A = 1/2 . (1/2 – 1/(99 . 100))` `A = 1/(2 . 2) – 1/(2 . 99 . 100)` `A = 1/4 – 1/19800` `A = 4949/19800` Trả lời
Đáp án:
`4949/19800`
Giải thích các bước giải:
`A` `=` `1/1` `.` `2.3` `+` `1/2` `.` `3` `.` `4` `+` `1/3` `.` `4` `.` `5` `+` `…` `+` `1/ 98.99.100`
`=` `1/2` `-` `1/2.3` `+` `1/2.3` `-` `1/3.4` `+` …. `1/98.99` `-` `1/99.100`
`=` `1/1.2` `-` `1/99.100`
`=` `4949/19800`
$#Đào$
`A = 1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))`
`A = 1/2 . 2 . (1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))`
`A = 1/2 . (2 . 1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))`
`A = 1/2 . (2/(1 . 2 . 3) + 2/(2 . 3 . 4) + 2/(3 . 4 . 5) + … + 2/(98 . 99 . 100))`
`A = 1/2 . (1/(1 . 2) – 1/(2 . 3) + 1/(2 . 3) – 1/(3 . 4) + … + 1/(98 . 99) – 1/(99 . 100))`
`A = 1/2 . (1/(1 . 2) – 1/(99 . 100))`
`A = 1/2 . (1/2 – 1/(99 . 100))`
`A = 1/(2 . 2) – 1/(2 . 99 . 100)`
`A = 1/4 – 1/19800`
`A = 4949/19800`