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

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

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

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

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

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

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

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

=1+1/2-1/12

=3/2-1/12

=17/12

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 \(A=\dfrac{29}{24}\)

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

anusa ikuy

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

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

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

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

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

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

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

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

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

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

\(< =>2A=\frac{5}{2}-\frac{1}{12}=\frac{29}{12}\)

\(< =>A=\frac{29}{12}.\frac{1}{2}=\frac{29}{24}\)

Các bạn giúp mình với

A , 10 số đầu tiên là : 1/2.4 + 1/4.6 + 1/6.8 + ...... + 1/20.22

= 1/2.( 2/2.4 + 2/4.6 + ..... + 2/20.22 )

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

= 1/2.( 1/2-1/22 )

= 1/2. 10/22

= 10/44

B , Vì 2000 ko viết về được dạng tích của 2 số chẵn liên tiếp nên 1/2000 ko thuộc dãy trên

Tk mk nha

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

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

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

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

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

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

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

Là 1 phần 4 + 1phan 8+ va cu nhu the

                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 !!! ^_^