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12 tháng 8 2015

\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+...+\frac{1}{25.27.29}\)

\(\Rightarrow4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{25.27.29}\)

\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{25.27}-\frac{1}{27.29}\)

\(=\frac{1}{3}-\frac{1}{783}=\frac{261}{783}-\frac{1}{783}=\frac{260}{783}\)

12 tháng 8 2015

A = \(\frac{1}{1.3.5}+\frac{1}{3.5.7}+....+\frac{1}{25.27.29}\)

A = \(\frac{1}{4}.\left(\frac{5-1}{1.3.5}+\frac{7-3}{3.5.7}+...+\frac{29-25}{25.27.29}\right)\)

A = \(\frac{1}{4}.\left(\frac{5}{1.3.5}-\frac{1}{1.3.5}+\frac{7}{3.5.7}-\frac{3}{3.5.7}+...+\frac{29}{25.27.29}-\frac{25}{25.27.29}\right)\)

A = \(\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{25.27}-\frac{1}{27.29}\right)\)

A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{27.29}\right)\)

A = \(\frac{1}{4}.\frac{206}{783}\)

A = \(\frac{65}{783}\)

1 tháng 5 2019

\(A\cdot2=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}...+\frac{1}{256}\right)\cdot2\)

\(=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}...+\frac{1}{128}\)

\(A\cdot2-A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}...+\frac{1}{128}-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\right)\)

\(A=1-\frac{1}{256}=\frac{255}{256}\)

1 tháng 5 2019

\(A=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\)

\(A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\)

\(2A=1+\frac{1}{2}+...+\frac{1}{2^7}\)

\(2A-A=\left(1+\frac{1}{2}+...+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\right)\)

\(A=1-\frac{1}{2^8}\)

\(A=\frac{2^8-1}{2^8}\)

\(A=\frac{255}{256}\)

4 tháng 7 2017

bài 1:

\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)

\(=\left(\frac{6}{11}+\frac{5}{11}\right)+\frac{1}{3}\)

\(=\frac{11}{11}+\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}\)

bài 2:

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)

\(=\left(\frac{1}{2}+\frac{1}{20}\right)+\left(\frac{1}{6}+\frac{1}{12}\right)\)

\(=\frac{11}{20}+\frac{1}{4}=\frac{11}{20}+\frac{5}{20}=\frac{15}{20}=\frac{3}{4}\)

bài 3: 

a) \(\frac{3}{2}\cdot\frac{4}{5}\cdot\frac{2}{3}=\left(\frac{3}{2}\cdot\frac{2}{3}\right)\cdot\frac{4}{5}=1\cdot\frac{4}{5}=\frac{4}{5}\)

b) \(\frac{6}{7}\cdot\frac{5}{3}\cdot\frac{7}{6}=\left(\frac{6}{7}\cdot\frac{7}{6}\right)\cdot\frac{5}{3}=1\cdot\frac{5}{3}=\frac{5}{3}\)

bài 4: 

a) \(\frac{2}{5}\cdot\frac{1}{4}+\frac{3}{4}\cdot\frac{2}{5}=\frac{2}{5}\cdot\left(\frac{1}{4}+\frac{3}{4}\right)=\frac{2}{5}\cdot1=\frac{2}{5}\)

b) \(\frac{6}{11}:\frac{2}{3}+\frac{5}{11}:\frac{2}{3}=\left(\frac{6}{11}+\frac{5}{11}\right):\frac{2}{3}=1:\frac{2}{3}=\frac{3}{2}\)

4 tháng 7 2017

Bài 1: 

  6/11 + 1/3 + 5/11 

= ( 6/11 + 5/11) + 1/3

= 11/11 + 1/3

= 1 + 1/3 

= 3/3 +1/3  

= 4/3 

Bài 2: 

1/2 + 1/6 + 1/12 + 1/20 

= ( 1/2 + 1/6 + 1/12 ) + 1/20 

= ( 6/12 + 2/12 + 1/12 ) + 1/20 

=9/12 + 1/20 

= 3/4 +1/20  

= 15/20 + 1/20 

= 16/20 = 4/5

 Bài 3:

a) \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\) \(=\left(\frac{3}{2}\times\frac{2}{3}\right)\times\frac{4}{5}\)\(=1\times\frac{4}{5}=\frac{4}{5}\) 

b)  \(\frac{6}{7}\times\left(\frac{5}{3}\times\frac{7}{6}\right)\) \(=\frac{6}{7}\times\frac{35}{18}\)\(=\frac{1\times5}{7\times3}=\frac{5}{21}\)   

Bài 4:

a) 2/5  x 1/4 + 3/4 x 2/5 

= 2/5 x ( 1/4  + 3/4) 

 = 2/5 x  1 

= 2/5

 b) 6/11 : 2/3 +5/11 : 2/3 

=  ( 6/11 + 5/11) x 3/2 

= 11/11 x 3/2  

= 1 x 3/2  

=  3/2  

....  

\(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(A=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

30 tháng 7 2020

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\\ \)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}\)

\(=\frac{4}{8}-\frac{1}{8}\\ =\frac{3}{8}\)

Chúc bn học thiệt giỏi nhé!

8 tháng 7 2017

a, \(\frac{2}{3}+\frac{2}{3}+\frac{6}{3}=\frac{10}{3}\)

b,\(\frac{3}{4}+\frac{3}{4}+\frac{3}{2}=\frac{6}{4}+\frac{3}{2}=\frac{3}{2}+\frac{3}{2}=\frac{6}{2}=3\)

18 tháng 1 2017

\(\frac{9}{11}\)nha kb đi

18 tháng 1 2017

lấy (1/3 + 1/15 +1/10 + 1/21 ) + (1/36 + 1/28 + 1/6) + (1/45 + 1/55)

      =  (4/50 + 3/70) + 2/100

      = 7/120 + 2/100

      = 9/220

15 tháng 7 2017

\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}=\frac{481}{280}\)

16 tháng 7 2017

Bạn phải giải ra 

27 tháng 8 2018

=127/128

~ chúc bn hok tốt ~

27 tháng 8 2018

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

\(=\frac{64}{128}+\frac{32}{128}+\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}\)

\(=\frac{126}{128}=\frac{63}{64}\)