Question

Tính nhanh:

E=1/99-1/99.98-1/97.96-.......-1/3.2-1/2.1

Answer 1

\(E=\frac{1}{99}-\frac{1}{99.98}-\frac{1}{97.96}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

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

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

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

\(=\)\(\frac{2}{99}-1\)

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