Question

Tính :\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\) = ?

Answer 1

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2006\cdot2007}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}=1-\frac{1}{2007}=\frac{2006}{2007}\)

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{2006}-\frac{1}{2007}\)

=\(1-\frac{1}{2007}\)

=\(\frac{2006}{2007}\)