Question

1/(1*20)+1/(2*3)+1/(3*4).+1/(2009*2010)=?

Answer 1

1/(1*2)+1/(2*3)+1/(3*4).+1/(2009*2010)

=[(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2009-1/2010)]

=(1-1/2010)

=2009/2010