= 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12

= 1/3 - 1/12 = 1/4

Sai rồi bạn ạ

Phải là 1/3 nhân 4 chứ ko phải 1/3x4

A  = 1 x 2 + 2 x 3 + ....... + 10 x 11

3A = 1 x 2 x 3 + 2 x 3 x 3 + ..........+ 10 x 11 x 3

3A = 1 x 2 x (3-0) + 2 x 3 x (4-1) + .......... + 10 x 11 x (12 -9)

3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ........... + 10 x 11 x 12 - 9 x 10 x 11

3A = (1 x 2 x 3 - 1 x 2 x 3) + ( 2 x 3 x 4 - 2 x 3 x 4) +............ + 10 x 11 x 12

3A = 10 x 11 x 12 = 1320

A = 1320 : 3 = 440

Gọi biểu thức trên là A, ta có :

A= 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101 A = 99x100x101 : 3 A = 333300

 

   \(\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\)

= \(\dfrac{1}{5}-\dfrac{1}{6}\times\dfrac{1}{6}-\dfrac{1}{7}\times\dfrac{1}{7}-\dfrac{1}{8}\times\dfrac{1}{8}-\dfrac{1}{9}\times\dfrac{1}{9}-\dfrac{1}{10}\)

= \(\dfrac{1}{5}-\dfrac{1}{10}\)  

= \(\dfrac{1}{10}\)

Bài tập cuối tuần 10

`1/[4xx5]+1/[5xx6]+1/[6xx7]+1/[7xx8]+1/[8xx9]+1/[9xx10]`

`=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10`

`=1/4-1/10`

`=10/40-4/40=6/40=3/20`

A= 5.(1/5.6+1/6.7+...+1/10.11)

A=5.(1/5-1/6+1/6-1/7+.....+1/10-1/11)

A=5.(1/5-1/11)

A=5.6/55=6/11

A=6/11<1

A<1

Ta có: \(A=\frac{5}{5x6}+\frac{5}{6x7}+\frac{5}{7x8}+\frac{5}{8x9}+\frac{5}{9x10}+\frac{5}{10x11}.\)

\(=5\left(\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}+...+\frac{1}{10x11}\right)\)

\(=5\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(=5\left(\frac{1}{5}-\frac{1}{11}\right)=5x\frac{6}{55}=\frac{6}{11}\)

Tra loi:

1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9

=1/2 - 1/3 + 1/3 - 1/4 +1/4 - 1/5 + 1/5 -1/6 +1/6 - 1/7 +1/7 -1/8+1/8 - 1/9

=1/2-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-(1/6-1/6)-(1/7-1/7)-(1/8-1/8)-1/9

=1/2-0-0-0-0-0-0-1/9

=1/2-1/9

=7/18

k cho minh nha!

thông điệp nhỏ 

hai tích nếu như ko muốn k

ai tích mình tích lại

cam on Mai Phuong nha!

\(\frac{1}{6x7}+\frac{1}{7x8}+\frac{1}{8x9}+\frac{1}{9x10}+\frac{1}{10x11}\)

\(=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{6}-\frac{1}{11}=\frac{5}{66}\)

330 nha

1/1x2+1/2x3+1/3x4+..+1/9x10

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5+...-1/10

=1-1/10

=9/10