Giải thích các bước giải:
13/. (`1/(1.2)` + `1/(3.4)` + `1/(5.6)` + ... + `1/(49.50)`) : (`(30)/(26)`+`(31)/(27)` + `(32)/(28)` + ... + `(54)/(50)` $-25)$
Đặt A = (`1/(1.2)` + `1/(3.4)` + `1/(5.6)` + ... + `1/(49.50)`)
= $(1+$`1/3`+ `1/5` + `1/7` + ... + `1/(49)`) - (`1/2` - `1/4` - `1/6` - `1/8` - `1/(50)`)
= $(1+$ `1/2`+ `1/3`+ ... + `1/(49)` + `1/(50)`) - 2.(`1/2` + `1/4` + `1/6` + `1/8` + ... + `1/(50)`)
= $(1+$ `1/2`+ `1/3` + ... + `1/(50)`) - (1+ `1/2`+ `1/3` + ... + `1/(25)`)
= `1/(26)` + `1/(27)` + `1/(28)` +... + `1/(50)`
B = (`(30)/(26)`+`(31)/(27)` + `(32)/(28)` + ... + `(54)/(50)` $-25)$
= [(`(30)/(26)`$-1)+($`(31)/(27)`$-1)+($`(32)/(28)` $-1)+...+$ `(54)/(50)` $-1)]$
= (`4/(26)`+ `4/(27)` + `(4)/(28)` + ... + `4/(50)`)
= 4.(`1/(26)` + `1/(27)` + `1/(28)` +... + `1/(50)`)
⇒ (`1/(1.2)` + `1/(3.4)` + `1/(5.6)` + ... + `1/(49.50)`) : (`(30)/(26)`+`(31)/(27)` + `(32)/(28)` + ... + `(54)/(50)` $-25)$
= `1/(26)` + `1/(27)` + `1/(28)` +... + `1/(50)` : 4.(`1/(26)` + `1/(27)` + `1/(28)` +... + `1/(50)`)
= `1/4`
14/. (`(100)/1` + `(99)/2` + `(98)/3` + ... + `2/(99)` + `1/(100)`) : (`1/4` + `1/6` + `1/8` + ... + `1/(202)`)
= $(100+$ `(99)/2` + `(98)/3` + ... + `2/(99)` + `1/(100)`) : (`1/4` + `1/6` + `1/8` + ... + `1/(202)`)
= $(1+$ `(99)/2`$+1+$ `(98)/3`$ +...+1+$`2/(99)`$)+(1+$`1/(100)`) : `2/2`.(`1/4` + `1/6` + `1/8` + ... + `1/(202)`)
= `(101)/(101)` + `(101)/2` + `(101)/3` + ... + `(101)/(99)`) + `(101)/(100)`) : `1/2`.(`2/4` + `2/6` + `2/8` + ... + `2/(202)`)
= $101.($`1/(101)` + `1/2` + `1/3` + ... + `1/(99)`) + `1/(100)`) : `1/2`.(`1/2` + `1/3` + `1/4` + ... + `1/(101)`)
= $101.($`1/2` + `1/3` + ... + `1/(99)` + `1/(100)`+`1/(101)`) : `1/2`.(`1/2` + `1/3` + `1/4` + ... + `1/(101)`)
= $101$ : `1/2`
= $101.2$
= $202$
Chúc bạn học tốt
