Các bạn giúp mk với, mk sắp phải nộp rồi. Ai nhanh nhất mk k cho
\(-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-..........-\frac{1}{2.1}\)
\(=-\left(\frac{1}{100.99}+\frac{1}{99.98}+\frac{1}{98.97}+..........+\frac{1}{2.1}\right)\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+........+\frac{1}{97.98}+\frac{1}{98.99}+\frac{1}{99.100}\right)\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(=-\left(1-\frac{1}{100}\right)=-\frac{99}{100}\)
\(=-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\right)\)
\(=-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=-\left(1-\frac{1}{100}\right)\)
\(=-\left(\frac{99}{100}\right)=\frac{-99}{100}\)
\(-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{2.1}\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)=-\left(1-\frac{1}{100}\right)=-\frac{99}{100}\)
