Question

求1/(x+1)(x+2)+1/(x+3)(x+4)+...+1/(x+1999)(x+2000)的值

Answer 1

=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)...+1/(x+1998)-1/(x+1999)+1/(x+1999)-1/(x+2000)

=1/(x+1)-1/(x+2000)

=1999/(x+1)(x+2000)

=1999/(x^2+2001x+2000)