Question

1/6+1/12+1/20+1/30+···+1/2005X2006=?

Answer 1

1/6+1/12+1/20+1/30+···+1/2005X2006

=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(2005X2006)

=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+...+(1/2005-1/2006)

=1/2-1/2006

=501/1003