Question

计算1／x(x+2) +1／(x+2)(x+4) +1／(x+4)(x+6)+...+1／(x+2010)(x+2012

Answer 1

1／x(x+2) +1／(x+2)(x+4) +1／(x+4)(x+6)+...+1／(x+2010)(x+2012)

=(1/x-1/(x+2)+1/(x+2)-1/(x+4)+...+1/(x+2010)-1/(x+2012))/2

=(1/x-1/(x+2012))/2

=1006/x(x+2012)