Question

\(\frac{2006}{1.2}\)+\(\frac{2006}{2.3}\)+...+\(\frac{2006}{2006.2007}\)

Answer 1

\(\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}\)

\(=2006.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)\)

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

\(=2006.\left(1-\frac{1}{2007}\right)\)

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

\(=\frac{2006^2}{2007}\)

Answer 2

\(=\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}\)

\(=2006 \left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)\)

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

\(=2006.\left(1-\frac{1}{2007}\right)\)

\(=2006.\frac{2006}{2007}=\frac{4024036}{2007}\)

Answer 3

Ta có: \(\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}\)

\(=2006.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)\)

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

\(=2006.\left(1-\frac{1}{2007}\right)\)

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

\(=\frac{4024036}{2007}\)