Question

如何化简下列算式1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005) 如何求

Answer 1

1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005)

=1/x + 1/x -1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+2004)-1/(x+2005)

=1/x+1/x-1/(x+2005)

= [2(x+2005)-x]/[ x(x+2005)]

=(x+4010)/[ x(x+2005)]

同理

1/x(x+2) =1/2 [1/X-1/(X+2)]