Question

\(x-\left(\frac{3^2}{8.11}+\frac{3^2}{11.14}+.......+\frac{3^2}{1997.2000}\right)=\frac{-1}{2}\)

Answer 1

Ta có : 

\(x-\left(\frac{3^2}{8.11}+\frac{3^2}{11.14}+...+\frac{3^2}{1997.2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{1997.2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{1997}-\frac{1}{2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3\left(\frac{1}{8}-\frac{1}{2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3.\frac{249}{2000}=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-\frac{747}{2000}=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x=\frac{-1}{2}+\frac{747}{2000}\)

\(\Leftrightarrow\)\(x=\frac{-253}{2000}\)

Vậy \(x=\frac{-253}{2000}\)

Chúc bạn học tốt ~ 

Answer 2

cảm ơn nhé

Answer 3

x - 3( \(\frac{3}{8.11}\)+\(\frac{3}{11.14}\)+.................+ \(\frac{3}{1997.2000}\)) = \(\frac{-1}{2}\)

x - 3(\(\frac{1}{8}\)-  \(\frac{1}{11}\)+ \(\frac{1}{11}\)- \(\frac{1}{14}\)+..................+ \(\frac{1}{1997}\)- \(\frac{1}{2000}\)) =\(\frac{-1}{2}\)

x  - 3.\(\frac{249}{2000}\)= \(\frac{-1}{2}\)

x -  \(\frac{747}{2000}\)=\(\frac{-1}{2}\)

x                      =\(\frac{-1}{2}+\frac{747}{2000}\)

x                         =\(\frac{-253}{2000}\)

                        Vậy x = \(\frac{-253}{2000}\)