Bài làm:

\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{9.10}\)

\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=2\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{10-9}{9.10}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{10}\right)=2.\frac{4}{10}=\frac{4}{5}\)

330 nha

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

 

1 x 2 = 2 

5 x 6 = 30 

2 x 3 = 6 

6 x 7 = 42 

3 x 4 = 12 

7 x 8 = 56 

4 x 5 = 20 

8 x 9 = 72 

HT

TL

1x2=2           2x3=6               3x4=12                     4x5=20

5x6=30             6x7=42                    7x8=56                      8x9=72

nha

HT

2                     6                         12                                20

30                    42                        56                                72 

k mình nha !!

= 9/10

k nha

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!

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{9.10}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{9}{10}\)

chúc bn học tốt

\(1,27+2,77+4,27+5,77+...+31,27+32,47\)

\(=\left(1,27+32,77\right)+\left(2,77+31,27\right)+....+\left(16,27+17,77\right)\)

\(=34,04+34,04+....+34,04\)( 11 số hạng)

\(=34,04.11=374,44\)

chúc bn học tốt

 b)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{10}{10}-\frac{1}{10}\)

\(=\frac{9}{10}\)

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

Ta có: \(C=\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}\)

\(\Leftrightarrow C=2\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\right)\)

\(\Leftrightarrow C=2\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)

\(\Leftrightarrow C=2\left(1-\dfrac{1}{7}\right)=\dfrac{2.6}{7}=\dfrac{12}{7}\)