如何化简下列算式1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005) 如何求解下面的分_数学解答

如何化简下列算式1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005) 如何求解下面的分式方程1/x(x+2)+1/(

人气：196 ℃　时间：2020-05-23 20:17:20

解答

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)]