已知x=100,求x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+99)(x+100)分之1_数学解答

已知x=100,求x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+99)(x+100)分之1

人气：472 ℃　时间：2019-08-25 08:15:28

解答

1/X(X+1)+1/(x+1)(x+2)+.+1/(x+99)(x+100)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+99)-1/(x+100)
=1/x-1/(x+100)
=1/100-1/(100+100)
=1/200