A = 1/2 - 1/3 - 1/4 + 1/3 - 1/4 - 1/5 + 1/4 - 1/5 - 1/6

A = 1/2 - 1/6

A = 1/3

k mk nha. ths bn nhìu nha

A = 1/2.3 - 1/ 3.4 + 1/3.4 - 1/4.5 + 1/4.5 -1/5.6

    = 1/2.3 - 1/5.6

    = 1/6 - 1/30

    =  2/15

Vậy A = 1/15

* Công thức : 

\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\left(\frac{3}{6}-\frac{1}{6}\right)=\frac{1}{2}.\frac{2}{6}=\frac{1}{6}=\frac{1}{1.2.3}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{20.21.22}\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{20.21}-\frac{1}{21.22}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{21.22}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{462}\right)\)

\(=\frac{1}{2}.\left(\frac{231}{462}-\frac{1}{462}\right)\)

\(=\frac{1}{2}.\frac{230}{462}\)

\(=\frac{115}{462}\)

Chúc bạn học tốt !!! 

Bạn có thể tham khảo tại :

Câu hỏi tương tự

Chúc bạn học giỏi =/

\(2S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(2S=\frac{1}{2}-\frac{1}{9900}\)

\(2S=\frac{4949}{9900}\)

\(S=\frac{4949}{19800}\)

Ta xét : \(\frac{1}{1.2}-\frac{1}{2.3}=\frac{2}{1.2.3}\)

\(\frac{1}{2.3}-\frac{1}{3.4}=\frac{2}{2.3.4}\)

...

\(\frac{1}{98.99}-\frac{1}{99.100}=\frac{2}{98.99.100}\)

Ta có : 2S = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

=> 2S = \(\frac{1}{1.2}-\frac{1}{99.100}\)

=> 2S = \(\frac{4949}{9900}\)

=> S = \(\frac{4949}{19800}\)

2S=\(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{98.99.100}\)

2S= \(1-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)2S= 1- \(\dfrac{1}{100}\)

2S= \(\dfrac{99}{100}\)

S= \(\dfrac{99}{100}.\dfrac{1}{2}\)

S=\(\dfrac{198}{100}\)

A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 20.21.22

4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 20.21.22.4

4A = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 20.21.22.(23 - 19)

4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 20.21.22.23 - 19.20.21.22

4A = 20.21.22.23

A = 20.21.22.23 : 4

A = 53130

Đặt A = 1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 +...+ 20.21.22

\(\Rightarrow4A=1.2.3.4+2.3.4.4+3.4.5.4+4.5.6.4+...+20.21.22.4\)

       \(=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+4.5.6.\left(7-3\right)+...+20.21.22.\left(23-19\right)\)  

        = 1.2.3.4 + 2.3.4.5  -1.2.3.4 + 3.4.5.6 - 2.3.4.5 + 4.5.6.7 - 3.4.5.6 +...+ 20.21.22.23 - 19.20.21.22

        =    20.21.22.23

        =  212520

_Hok tốt_

!!!        

1/2x3x4 + 1/3x4x5 + 1/4x5x6 + 1/5x6x7 + ..... + 1/8x9x10

= { 2/2x3x4 + 2/3x4x5 + 2/4x5x6 + .... + 2/8x9x10 } : 2

= { 4-2/2x3x4 + 5-3/3x4x5 + 6-4/4x5x6 + .... + 10-8/8x9x10 } : 2

= { 4/2x3x4 - 2/2x3x4 + 5/3x4x5 - 3/3x4x5 + ... + 10/8x9x10 - 8/8x9x10 } : 2

= { 1/2x3 - 1/3x4 + 1/3x4 - 1/4x5 + ... + 1/8x9 - 1/9x10 } : 2

=  { 1/2x3 - 1/9x10 } :2

=  { 1/6 - 1/90 } : 2

= 14/90 :  2

= 7/90

B=1.2.3+2.3.4+4.5.6+....+20.21.22

=>4B=4(1.2.3+2.3.4+3.4.5+...+20.21.22)

=>4B=1.2.3.4+2.3.4.4+3.4.5.4+...+20.21.22.4

=>4B=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+20.21.22(23-19)

=>4B=1.2.3.4+2.3.4.5-2.3.4+3.4.5.6-2.3.4.5+...+20.21.22.23-19.20.21.22

=>4B=20.21.22.23

=>4B=212520

=>B=53130

mình nha

Đặt A = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 + 4 . 5 . 6 + ... + 20 . 21 . 22

=> 4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 4 + 3 . 4 . 5 . 4+ 4 . 5 . 6 . 4 + ... + 20 . 21 . 22 . 4

=> 4A = 1 . 2 . 3 . ( 4 - 0 ) + 2 . 3 . 4 . ( 5 - 1 ) + 3 . 4 . 5 . ( 6 - 2 ) + 4 . 5 . 6 . ( 7 - 3 ) + ... + 20 . 21 . 22 . ( 23 - 19 )

=> 4A = 1 . 2 . 3 . 4 - 0 + 2 . 3 . 4 . 5 - 1 . 2 . 3 . 4 + 3 .4 . 5 . 6 - 2 . 3 . 4 . 5 + 4 . 5 . 6 . 7 - 3 . 4 . 5 . 6 + ... + 20 . 21.22.23 - 19.20.21.22

=> 4A = 0 + 20 . 21 . 22 . 23 

=> 4A = 212520

=> A = \(\frac{212520}{4}=53130\)