Tính A

\(A=2\frac{2}{35}^3-\frac{2^3}{63}-\frac{2}{99}^3-\frac{2}{143}^3-\frac{2}{195}^3-\frac{2}{255}^3-\frac{2}{323}^3\)

giải cả bài nha

loại trừ bớt đi rùi tìm x 

\(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{x.\left(x+2\right)}=\frac{24}{35}\)

\(\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{24}{35}\)

\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{x+2}\right)=\frac{24}{35}\)

\(\frac{3}{10}-\frac{3}{2x+4}=\frac{24}{35}\)

\(\frac{3}{2x+4}=\frac{-27}{70}\)

tự làm nốt

\(\frac{3}{35}+\frac{3}{63}+\frac{3}{99}+....+\frac{3}{x\left(x+2\right)}=\frac{24}{35}\)

\(\Leftrightarrow3\left(\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+....+\frac{1}{x\left(x+2\right)}\right)=\frac{24}{25}\)

\(\Leftrightarrow3\left(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{x\left(x+2\right)}\right)=\frac{24}{35}\)

\(\Leftrightarrow3\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+....+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{24}{35}\)

\(\Leftrightarrow3\left(\frac{1}{5}-\frac{1}{x+2}\right)=\frac{24}{35}\)

\(\Leftrightarrow\frac{3}{5}-\frac{3}{x+2}=\frac{24}{35}\)

\(\Leftrightarrow\frac{3}{x+2}=\frac{3}{5}-\frac{24}{35}\)

\(\Leftrightarrow\frac{3}{x+2}=\frac{21-24}{35}\)

\(\Leftrightarrow\frac{3}{x+2}=\frac{3}{-35}\)

\(\Rightarrow x+2=-35\Leftrightarrow x=-35-2\Leftrightarrow x=-37\)

Vậy \(x=-37\)

\(A=\frac{2}{3}+\frac{14}{15}+\frac{34}{35}+\frac{62}{63}+\frac{98}{99}+\frac{142}{143}\)

\(=\left(1-\frac{1}{3}\right)+\left(1-\frac{1}{15}\right)+\left(1-\frac{1}{35}\right)+\left(1-\frac{1}{63}\right)+\left(1-\frac{1}{99}\right)+\left(1-\frac{1}{143}\right)\)

\(=\left(1+1+1+1+1+1\right)-\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)

\(=6-\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\right)\)

\(=6-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=6-\left(1-\frac{1}{13}\right)\)

\(=6-1+\frac{1}{13}\)

\(=5+\frac{1}{13}\)

\(=\frac{66}{13}\)

Mk sửa lại 1 tí nha dòng thứ 5 :

\(A=6-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=6-\frac{1}{2}\left(1-\frac{1}{13}\right)\)

\(=6-\frac{1}{2}.\frac{12}{13}\)

\(=6-\frac{6}{13}=\frac{72}{13}\)

Mong bn bỏ qua nha