Question

M=1/6+1/12+1/20+...+1/2009.2010

Answer 1

\(M=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2009.2010}\)

        \(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2009}-\frac{1}{2010}\)

        \(=\frac{1}{2}-\frac{1}{2010}=\frac{502}{1005}\)

Answer 2

\(M=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)

\(M=\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2009}-\frac{1}{2010}\)

\(M=\frac{1}{2}-\frac{1}{2010}\)

\(M=\frac{1004}{2010}=\frac{502}{1005}\)