Question

Tính: 1/100 - 1/100.99 - 1/99.99 - ... - 1/3.2 - 1/ 2.2 = ?

Answer 1

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

=\(\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\right)\)

=\(\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\right)\)

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

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

=\(\frac{-49}{50}\)