Question

(\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\) ) \(-X\) = \(\frac{-100}{99}\)

Answer 1

Ta có : 

\(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-x=\frac{-100}{99}\)

\(\Leftrightarrow\)\(\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)-x=\frac{-100}{99}\)

\(\Leftrightarrow\)\(\left(1-\frac{1}{99}\right)-x=\frac{-100}{99}\)

\(\Leftrightarrow\)\(\frac{98}{99}-x=\frac{-100}{99}\)

\(\Leftrightarrow\)\(x=\frac{98}{99}+\frac{100}{99}\)

\(\Leftrightarrow\)\(x=\frac{198}{99}\)

\(\Leftrightarrow\)\(x=2\)

Vậy \(x=2\)

Chúc bạn học tốt ~ 

Answer 2

98/99 - x = -100/99

x = 98/99 - -100/99

x = 198/99

Answer 3

\(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-X=\frac{-100}{99}\)

\(\left(1-\frac{1}{3}+\frac{1}{3}+-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)-X=\frac{-100}{99}\)

\(\left(1-\frac{1}{99}\right)-X=\frac{-100}{99}\)

\(\frac{98}{99}-X=\frac{-100}{99}\)

             \(X=\frac{98}{99}-\frac{-100}{99}\)

             \(X=\frac{198}{99}\)

              \(X=2\)