Đặt \(A=\frac{2006}{1\cdot2}+\frac{2006}{2\cdot3}+...+\frac{2006}{2006\cdot2007}\)
\(2006A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2006\cdot2007}\)
\(2006A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}\)
\(2006A=\frac{1}{1}-\frac{1}{2007}\)
\(2006A=\frac{2006}{2007}\)
\(A=\frac{2006}{2007}\div2006\)
\(A=\frac{1}{2007}\)
Vậy giá trị của biểu thức bằng 1/2007
* Không chắc nha *
Sửa đề : \(A=\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}\)
\(2006A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\)
\(2006A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}\)
\(2006A=1-\frac{1}{2007}\)
\(2006A=\frac{2006}{2007}\)
\(A=\frac{2006}{2007}:2006=\frac{2006}{2007}.\frac{1}{2006}=\frac{1}{2007}\)
