Question

1/1•2+1/2•3+1/3•4+...+1/2009•2010 giải thích giùm mình

Answer 1

Đặt \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)

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

\(\Rightarrow A=1-\frac{1}{2010}=\frac{2010}{2010}-\frac{1}{2010}=\frac{2009}{2010}\)

Vậy \(A=\frac{2009}{2010}\)

Answer 2

1/1*2+1/2*3+........+1/2009*2010

=1-1/2+1/2-1/3+..........+1/2009-1/2010

=1-1/2010

=2009/2010