=1 - 1/2 + 1/2 - 1/3 + ..... + 1/2009 - 1/2010
=1 - 1/2010
=2009/2010
1-1/2+1/2-1/3+1/3-1/4+... +1/2009-1/2010
1-1/2010=2009/2010
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2009}-\frac{1}{2010}\)
\(=\frac{1}{1}-\frac{1}{2010}\)
\(=\frac{2009}{2010}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+...................+\frac{1}{2009.2010}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+................+\frac{1}{2009}-\frac{1}{2010}\)
=\(1-\frac{1}{2010}\)
=\(\frac{2009}{2010}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2009}-\frac{1}{2010}\)
= \(1-\frac{1}{2010}=\frac{2009}{2010}\)
=1 - 1/2 + 1/2 - 1/3 + ..... + 1/2009 - 1/2010
=1 - 1/2010
=2009/2010
