1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+99)(x+100)

问题描述:

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+99)(x+100)

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+99)(x+100) =[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+…… +[1/(x+99)-1/(x+100)]=1/x-1/(x+100)=100/x(x+100)