1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+2007)(x+2_数学解答

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+2007)(x+2008)求当X=1时,该式的值
请给出准确步骤

人气：384 ℃　时间：2020-04-15 01:28:14

解答

1/x(x+1)=1/x-1/(x+1)1/(x+1)(x+2)=1/(x+1)-1/(x+2)..1/(x+2007)(x+2008)=1/(x+2007)-1/(x+2008)所有式子相加得,右边两两相消1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+2007)(x+2008)=1/x-1/(x+1)...