Question

tính hợp lí   1/99 - 1/99.98 - 1/98.97 - 1/ 97.96 - ... -1/3.2 - 1/2.1

Answer 1

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

= \(\frac{1}{99}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{98.99}\right)\)

= \(\frac{1}{99}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{98}-\frac{1}{99}\right)\)

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

= \(\frac{1}{99}-\frac{98}{99}\)

= \(\frac{-97}{99}\)