Question

1. Tính nhanh :

     A = \(\frac{1}{100}\) - \(\frac{1}{100.99}\) - \(\frac{1}{99.98}\) - \(\frac{1}{98.97}\) - ... - \(\frac{1}{3.2}\) - \(\frac{1}{2.1}\)

Answer 1

\(A=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(A=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+..+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(A=\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

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

\(A=\frac{1}{100}-\frac{99}{100}\)

\(A=-\frac{98}{100}=-\frac{49}{50}\)