Question

Có ai giúp mình giải bài này với ?

Tính  \(M=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{2009\cdot2010}\)

Answer 1

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

M=1/2.3+1/3.4+1/4.5+...+1/2009.2010

M=1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010

M=1/2-1/2010

M=1004/2010

Tự rút gọn bn nha

Answer 2

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

M=1/2.3+1/3.4+1/4.5+.........+1/2009.2010

M=1/2-1/3+1/3-1/4+1/4-1/5+........+1/2009-1/2010

M=1/2-1/2010

=502/1005

Answer 3

\(M=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{2009\cdot2010}\)

\(\Rightarrow M=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2009\cdot2010}\)

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

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