\(\frac{1}{1}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+...+\frac{1}{79}\cdot\frac{1}{80}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{79\cdot80}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+...+\frac{1}{79}-\frac{1}{80}\)

\(=1-\frac{1}{80}\)

\(=\frac{79}{80}\)

`@Fù`

`=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(72×73)`

`=1/1-1/2+1/2-1/3+...+1/72-1/73`

`=1-1/73`

`=72/73`

\(a)\frac{1}{5}\times\frac{1}{2}:\frac{1}{3}=\frac{1}{5}\times\frac{1}{2}\times\frac{3}{1}=\frac{1\times1\times3}{5\times2\times1}=\frac{1\times3}{5\times2}=\frac{3}{10}\)

\(b)\frac{2}{9}:\frac{2}{3}\times\frac{1}{2}=\frac{2}{9}\times\frac{3}{2}\times\frac{1}{2}=\frac{2\times3\times1}{9\times2\times2}=\frac{1\times1\times1}{3\times1\times2}=\frac{1}{6}\)

\(c)\frac{1}{2}\times\frac{1}{3}+\frac{1}{4}=\frac{1}{6}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{2+3}{12}=\frac{5}{12}\)

d, Tương tự như câu c

P/S : Bất phương trình????

\(\frac{1}{5}\times\frac{1}{2}:\frac{1}{3}\)

\(=\frac{1}{10}\times\frac{3}{1}\)

\(=\frac{3}{10}\)

tích đúng mình giải cho

= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5 x 6

= (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6)

= 1 - 1/6

= 5/6

nha,mơn nhìu

Tìm y biết 3 x y x (1/1 x 1/2 + 1/2 x 1/3 + 1/3 x 1/4 + 1/4 x 1/5 + 1/5 x 1/6) = 3/4

Ta thấy: 1/1x1/2 = 1/1-1/2  ;  1/2x1/3 = ½-1/3  ;  1/3x1/4=1/3-1/4  ;  1/4x1/5=1/4-1/5  ;  1/5x1/6=1/5-1/6

Nên

1/1 x 1/2 + 1/2 x 1/3 + 1/3 x 1/4 + 1/4 x 1/5 + 1/5 x 1/6 =

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

Hay 3 x y x 5/6 = 3/4

y x 15/6 = 3/4

y= 3/4 : 15/6

y  =  3/10

sợ sai lắm

(1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007) = ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16) x .....x ( 1 - 1/4028049) = 3/4 x 8/9 x 15/16 x .....x 4028048 / 4028049 = 3 x 8 x 15 x .....x 4028048 / 4 x 9 x 16 x ......x 4028049 = 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x 2008 / 2x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007 = ( 1 x 2 x 3 x .....x 2006) x ( 3 x 4 x 5 x .....x 2008) / ( 2 x 3 x 4 x ....x 2007) x ( 2 x 3 x 4 x ....x 2007) = 2008 / 2007 x 2 = 1004 / 2007

(1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007)
= ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16) x .....x ( 1 - 1/4028049)
= 3/4 x 8/9 x 15/16 x .....x 4028048 / 4028049
= 3 x 8 x 15 x .....x 4028048 / 4 x 9 x 16 x ......x 4028049
= 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x 2008 / 2x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007
= ( 1 x 2 x 3 x .....x 2006) x ( 3 x 4 x 5 x .....x 2008) / ( 2 x 3 x 4 x ....x 2007) x ( 2 x 3 x 4 x ....x 2007)
= 2008 / 2007 x 2
= 1004 / 2007

câu 2 đề sai

à đề câu 2 là:1+1/3+1/6+1/10+...+1/x+(x+1):2

Tính 

a ) 5/2 x 1/3 + 1/4

= 5/5+1/4

=13/12

b)5/2 +  1/3 x 1/4

= 5/2 + 1/12

= 31/12

c ) 5/2 -1/3 :1/4

= 5/2  - 4/3

= 7/6

tk mk nha ( nếu đúng )

hihi mơn nha !!!!!!!!!!

a. = (5/2x2/3) +1/4

    = 5/3+1/4= 23/12

b. = 5/2+( 1/3x1/4)

    = 5/2+1/12

    =31/12

c. =5/2-( 1/3:1/4)

    = 5/2-4/3

    = 7/6