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19 tháng 7 2016

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}+\frac{1}{168}\)

\(=\frac{1}{4}.\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)

\(=\frac{1}{4}.\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

\(=\frac{1}{4}.\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\left(1+1-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\left(2-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\frac{13}{7}=\frac{13}{28}\)

19 tháng 7 2016

Là 1 phần 4 + 1phan 8+ va cu nhu the

19 tháng 7 2016

                Ta có : 

           Đặt    \(A=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}+\frac{1}{168}\)

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

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

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

                \(2A=\frac{1}{2}-\frac{1}{14}\)

                \(2A=\frac{7}{14}-\frac{1}{14}=\frac{3}{7}\)

                  \(A=\frac{3}{7}:2=\frac{3}{14}\)

           => \(\frac{1}{4}+\frac{3}{14}=\frac{7}{28}+\frac{6}{28}=\frac{13}{28}\)

           Ủng hộ mk nha !!! ^_^

           

          

           

2 tháng 3 2023

\(A=1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

\(=1+\dfrac{1}{2\times4}+\dfrac{1}{4\times6}+\dfrac{1}{6\times8}+\dfrac{1}{8\times10}+\dfrac{1}{10\times12}\)

\(=1+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{12}\)

\(=1+\dfrac{1}{2}-\dfrac{1}{12}=\dfrac{17}{12}\)

26 tháng 4 2019

A=1/8+1/24+1/48+1/80+1/120+1/168+1/224=>2A=2/8+2/24+2/48+2/80+2/120+2/168+2/224

2A=2/2*4+2/4*6+2/6*8+2/8*10+2/10*12+2/12*14+2/14*16

2A=1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12+1/12-1/14+1/14-1/16

2A=1/2-1/16

2A=7/16

A=7/16:2

A=7/32

9 tháng 2 2018

A = 1 + 1/2.4 + 1/4.6 + ...... + 1/10.12

2A = 2 + 2/2.4 + 2/4.6 + ...... + 2/10.12

     = 2 + 1/2 - 1/4 + 1/4 - 1/6 + ...... + 1/10 - 1/12

     = 2 + 1/2 - 1/12 = 29/12

=> A = 29/12 : 2 = 29/24

P/S : Tham khảo nha

9 tháng 2 2018

anusa ikuy

28 tháng 2 2018

\(1\frac{5}{24}=\frac{29}{24}\)

28 tháng 2 2018

A = 1 + 1/2.4 + 1/4.6 + 1/6.8 + 1/8.10 + 1/10.12

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

     = 2 + 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12

     = 2 + 1/2 - 1/12 = 29/12

=> A = 29/12 : 2 = 29/24

Tk mk nha

Ta có: \(A=1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

\(\Leftrightarrow2A=2+\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+\dfrac{2}{8\cdot10}+\dfrac{2}{10\cdot12}\)

\(\Leftrightarrow2A=2+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{12}\)

\(\Leftrightarrow2A=2+\dfrac{1}{2}-\dfrac{1}{12}\)

\(\Leftrightarrow2A=\dfrac{24}{12}+\dfrac{6}{12}-\dfrac{1}{12}\)

\(\Leftrightarrow2A=\dfrac{29}{12}\)

hay \(A=\dfrac{29}{24}\)

27 tháng 5 2022

`1/8+1/24+1/48+1/80+1/120`

`=1/[2xx4]+1/[4xx6]+1/[6xx8]+1/[8xx10]+1/[10xx12]`

`=1/2xx(2/[2xx4]+2/[4xx6]+2/[6xx8]+2/[8xx10]+2/[10xx12])`

`=1/2xx(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)`

`=1/2xx(1/2-1/12)`

`=1/2xx(6/12-1/12)`

`=1/2xx5/12=5/24`

\(\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

=\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{10.12}\)

=\(\dfrac{1}{2}.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{10.12}\right)\)

=\(\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{12}\right)\)

=\(\dfrac{1}{2}.\dfrac{5}{12}\)

=\(\dfrac{5}{24}\)

Dấu chấm(.)là nhân.

18 tháng 4 2019

49/48

5 tháng 5 2022

2a= 2/3+2/8+2/15+2/24+2/35+2/48+2/63+2/80= [2/( 1*3)+2/( 3*5)+2/( 5*7)+2/( 7*9)]+[2/(2*4)+2/(4*6)+2/(6*8)+2/(8*10)]= [1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9]+[1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10]= [1/1-1/9]+[1/2-1/10]= 8/9+2/5= 58/45 =>a= 29/45