Question

Tính nhanh :

1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/200.201

Answer 1

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{200.201}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)

=\(\frac{1}{2}-\frac{1}{201}\)

=\(\frac{199}{402}\)

Answer 2

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{200.201}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{200}-\frac{1}{201}\)

\(=\frac{1}{2}-\frac{1}{201}=\frac{199}{402}\)