A= \(\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)

A= \(\frac{2}{2}.\left(\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+\frac{1}{5.7}+\frac{1}{6.8}+\frac{1}{7.9}+\frac{1}{8.10}\right)\)

A=\(\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)

\(A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)

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

A= tự tính

Đáp án :

\(\frac{29}{45}\)

Đúng thì k nhé ^ ^

\(\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)

\(=\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)+\left(\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}\right)\)

\(=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)+\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)\)

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)+\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{9}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{10}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{9}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{1}{2}.\frac{8}{9}+\frac{1}{2}.\frac{2}{5}=\frac{1}{2}\left(\frac{8}{9}+\frac{2}{5}\right)=\frac{1}{2}.\frac{58}{45}=\frac{29}{45}\)

A=\(\frac{1}{3}\)+\(\frac{1}{8}\)+\(\frac{1}{15}\)+\(\frac{1}{24}\)+\(\frac{1}{35}\)+\(\frac{1}{48}\)+\(\frac{1}{63}\)+\(\frac{1}{80}\)

A=\(\frac{1}{2}\)(\(\frac{1}{1\cdot3}\)+\(\frac{1}{2\cdot4}\)+\(\frac{1}{3\cdot5}\)+\(\frac{1}{4.6}\)+\(\frac{1}{5.7}\)+\(\frac{1}{6.8}\)+\(\frac{1}{7.9}\)+\(\frac{2}{8.10}\))

A=\(\frac{1}{2}\)(1-1/3 +1/2-1/4 + 1/3 -1/5 +1/4-1/6 +1/5 - 1/7 +1/6 -1/8 +1/7 - 1/9 +1/8 - 1/10)

A= \(\frac{1}{2}\)(1 + 1/2 -1/9 -1/10)

A=\(\frac{29}{45}\)

\(A=\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)

\(=\frac{1}{1\times3}+\frac{1}{2\times4}+\frac{1}{3\times5}+\frac{1}{4\times6}+\frac{1}{5\times7}+\frac{1}{6\times8}+\frac{1}{7\times9}+\frac{1}{8\times10}\)

\(=\frac{1}{2}\times\left[\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}\right)+\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+\frac{2}{8\times10}\right)\right]\)

\(=\frac{1}{2}\times\left[\left(\frac{3-1}{1\times3}+\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+\frac{9-7}{7\times9}\right)+\left(\frac{4-2}{2\times4}+\frac{6-4}{4\times6}+\frac{8-6}{6\times8}+\frac{10-8}{8\times10}\right)\right]\)

\(=\frac{1}{2}\times\left[\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\right]\)

\(=\frac{1}{2}\times\left[\left(1-\frac{1}{9}\right)+\left(\frac{1}{2}-\frac{1}{10}\right)\right]\)

\(=\frac{29}{45}\)

\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}...1\frac{1}{80}\)

\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}...\frac{81}{80}\)

\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{9.9}{8.10}\)

\(=\frac{2.3.4...9}{1.2.3...8}.\frac{2.3.4...9}{3.4.5...10}\)

\(=9.\frac{2}{10}\)

\(=9.\frac{1}{5}=\frac{9}{5}\)

1 và 1 phần 3 . 1 và 1 phần 8 . 1 và 1 phần 15 . 1 và 1 phần 24  . 1 và 1 phần 35 . 1 và 1 phần 48 . 1 và 1 phần 63 . 1 và 1 phần 80 

= 4 phần 3 . 9 phần 8 . 16 phần 15 . 25 phần 24 . 36 phần 35 . 49 phần 48 . 64 phần 63 . 81 phần 80

= 3 phần 2 . 10 phần 9 . 15 phần 14 . 36 phần 35 

= 5 phần 3 . 54 phần 49 

= 90 phần 49 

1/100