解方程1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=1999/200_数学解答

解方程1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=1999/2000

人气：213 ℃　时间：2019-08-21 20:38:13

解答

1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/(x+1)-1/(x+100)
1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=1/(x+1)
1/(x+1)=1999/2000
x=1/1999