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13 tháng 8 2015

\(\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+\frac{3}{10.12}+\frac{3}{12.14}\)

=\(3.\left(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)

=\(\frac{3}{2}.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\right)\)

=\(\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)

=\(\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{14}\right)\)

=\(\frac{3}{2}.\left(\frac{7}{28}-\frac{2}{28}\right)\)

=\(\frac{3}{2}.\frac{5}{28}=\frac{15}{56}\)

4 tháng 5 2020

\(\sqrt[]{\frac{ }{ }\frac{ }{ }\hept{\begin{cases}\\\end{cases}}\hept{\begin{cases}\\\\\end{cases}}\orbr{\begin{cases}\\\end{cases}}^2}\)

19 tháng 2 2020

=>2A=2(1/2x4+1/4.6+1/6.8+1/8.10+1/10.12+1/12.14)

=> 2A=2/2.4 + 2/4.6 + 2/6.8 + 2/8.10 + 2/10.12 + 2/12.14

=> 2a =1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7

=> 2A =1-1/7

=>2A=16/17

=> A= 8/17

Mình chắc chắn . Chúc bạn học tốt

\(A=\frac{1}{2.4}\)\(+\frac{1}{4.6}\)\(+\frac{1}{6.8}\)\(+\frac{1}{8.10}\)\(+\frac{1}{10.12}\)\(+\frac{1}{12.14}\)

\(\Rightarrow2A=2.\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)

\(\Rightarrow2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{14}=\frac{7}{14}-\frac{1}{14}=\frac{6}{14}\)

\(\Rightarrow2A=\frac{6}{14}\)

\(\Rightarrow A=\frac{3}{14}\)

22 tháng 1 2017

\(\frac{5}{4.6}+\frac{5}{6.8}+\frac{5}{8.10}+...+\frac{5}{298.300}\)

\(=\frac{5}{2}\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{298}-\frac{1}{300}\right)\)

\(=\frac{5}{2}\left(\frac{1}{4}-\frac{1}{300}\right)=\frac{5}{2}.\frac{37}{150}=\frac{37}{60}\)

5 tháng 4 2015

Gọi biều thức trên là A, ta có:

A=(1/2.4+1/4.6+1/6.8+1/8.10+1/10.12)x=2

2A=(2/2.4+2/4.6+2/6.8+2/8.10+2/10.12)x=2

2A=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)x=2

2A=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)x=2

2A=(1/2-1/12)x=2

2A=5/12x=2

=>A=5/24x=1

=>x=1:5/24=24/5

 

5 tháng 4 2015

=>1/2.(5/12).x=1

5/24.x=1

x=1:5/24

x=24/5

lưu ý, 1/2.5/12 là tính xong phần 1/2.4 +...+1/10.12 rùi nhé

23 tháng 3 2017

\(B=\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+...+\frac{3}{20.22}\)

\(=\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+...+\frac{1}{20.22}\)

\(=\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{20}-\frac{1}{22}\right)\)

\(=\frac{1}{4}-\frac{1}{22}\)

\(=\frac{9}{44}\)

23 tháng 3 2017

A = 1111 x ( 1/2 - 1/3 - 1/6 )

A = 1111 x 0 = 0

B = 3/4 x 6 + 3/6 x 8 + 3/8 x 10 + ... + 3/20 x 22

B = 3/2 ( 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/20 - 1/22 )

B = 3/2 x ( 1/4 - 1/22 )

B = 3/2 x 9/44 = 27/88

19 tháng 6 2019

\(\frac{1.4}{4.6}+\frac{2.5}{6.8}+...+\frac{48.51}{98.100}\)

=> \(\frac{1}{4}.\left(\frac{1.4}{2.3}+\frac{2.5}{3.4}+...+\frac{48.52}{49.50}\right)\)

=> \(\frac{1}{4}.\left(\frac{2.3-2}{2.3}+\frac{3.4-2}{3.4}+...+\frac{49.50-2}{49.50}\right)\)

=> \(\frac{1}{4}.\left(1-\frac{2}{2.3}+1-\frac{2}{3.4}+...+1-\frac{2}{49.50}\right)\)

=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2.3}-\frac{1}{3.4}-\frac{1}{49.50}\right)\right]\)

=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\right]\)

=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2}-\frac{1}{50}\right)\right]\)

=> \(\frac{1}{4}.\left[48-2.\frac{12}{25}\right]\)

=> \(\frac{1}{4}.\frac{1176}{25}=\frac{249}{25}\)

7 tháng 3 2017

Đặt A = 8.10 + 10.12 + 12.14 + ....... + 98.100

=> 6A = 8.10.12 - 8.10.12 + 10.12.14 - 10.12.14 + ...... + 98.100.102

=> 6A =  98.100.102

=> A = 98.100.102/6

=> A = 166600

7 tháng 3 2017

c.1.2.3+2.3.4+4.5.6+5.6.7=6+24+120+210

                                      =30+120+210

                                      =150+210

                                      =360

3 tháng 4 2019

\(\frac{5}{4\cdot6}+\frac{5}{6\cdot8}+\frac{5}{8\cdot10}+...+\frac{5}{298\cdot300}\) 

\(=\frac{5}{2}\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{298}-\frac{1}{300}\right)\) 

\(=\frac{5}{2}\left(\frac{1}{4}-\frac{1}{300}\right)\) 

\(=\frac{5}{2}\cdot\frac{37}{150}\) 

\(=\frac{37}{60}\)

3 tháng 4 2019

\(\frac{5}{4.6}+\frac{5}{6.8}+\frac{5}{8.10}+...+\frac{5}{298.300}\)

\(\frac{5}{2}.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+...+\frac{2}{298.300}\right)\)

\(\frac{5}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{298}-\frac{1}{300}\right)\)

\(\frac{5}{2}.\left(\frac{1}{4}-\frac{1}{300}\right)\)

\(\frac{5}{2}.\frac{37}{150}\)

\(\frac{37}{60}\)

3 tháng 9 2017

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\)

\(2S=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\)

\(2S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{10}\)

\(2S=\frac{1}{2}-\frac{1}{10}\)

\(2S=\frac{2}{5}\)

\(S=\frac{2}{5}:2\)

\(S=\frac{1}{5}\)

3 tháng 9 2017

S = \(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\)

=> 2S = \(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\)

=> 2S = \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\)

=> 2S = \(\frac{1}{2}-\frac{1}{10}=\frac{5}{10}-\frac{1}{10}=\frac{4}{10}=\frac{2}{5}\)

=> S = \(\frac{2}{5}:2=\frac{2}{5}x\frac{1}{2}=\frac{1}{5}\)

17 tháng 3 2017

=3(1/2 -1/34)=3(17-1)/34=3.16/34=24/17

Đs: 24/17

17 tháng 3 2017

dễ

bằng 24/17

k cho mình nha