Question

Tính nhanh : 1/99. 100 -1/99.98-1/98.97-1/97.96-...-1/2.1

Answer 1

\(\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}-\frac{1}{97.96}-....-\frac{1}{2.1}\)

=\(\frac{1}{99}-\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{98.99}\right)\)

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

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

=\(\frac{1}{99}-\frac{98}{99}\)

=\(\frac{-97}{99}\)

Answer 2

\(\frac{-97}{99}\)