Question

1/1.2+1/2.3+1/3.4+...+1/2009.2010

Answer 1

= 1 - 1/2 . 1/2 -1/3 . 1/3 - 1/4 ... 1/2009 - 1/2010

= 1 - 1/ 2010

=1/2010

Answer 2

1/1.2+1/2.3+1/3.4+...+1/2009.2010

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

=1-1/2010

=2009/2010

Answer 3

=(1-1/2)+(1/2-1/3)+...+(1/9-1/10) 
=1-1/10 
=9/10

Answer 4

1/1.2+1/2.3+1/3.4+...+1/2009.2010

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

=1-1/2010

=2009/2010