Question

Tính hợp lí

1/200- 1/200.199- 1/199.198- .....-1/3.2- 1/2.1

Answer 1

\(\frac{1}{200}-\frac{1}{200.199}-\frac{1}{199.198}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(=\frac{1}{200}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{198.199}+\frac{1}{199.200}\right)\)

\(=\frac{1}{200}-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{198}-\frac{1}{199}+\frac{1}{199}-\frac{1}{200}\right)\)

\(=\frac{1}{200}-\left(1+\frac{1}{200}\right)\)

\(=\left(\frac{1}{200}-\frac{1}{200}\right)-1\)

\(=0-1\)

\(=-1\)