Question

观察下列各式：1/2=1/1*2=1/1-1/2；1/6=1/2*3=1/2-1/3；1/12=1/3*4=1/3-1/

Answer 1

1/a（a-1）+1/（a-1)(a-2)+...+1/(a-2008)(a-2009)

=1/(a-1)-1/a+1/(a-2)-1/(a-1)+……+1/(a-2009)-1/(a-2008)

=-1/a+1/(a-2009)

=1/(a-2009)-1/a

=2009/a(a-2009)