1/x(x+1)(x+2)+1/(x+1)(x+2)(x+3).+1/(x+98)(x+99)(x+100)=?_数学解答

1/x(x+1)(x+2)+1/(x+1)(x+2)(x+3).+1/(x+98)(x+99)(x+100)=?

人气：481 ℃　时间：2019-08-17 21:25:16

解答

1/x(x+1)(x+2)+1/(x+1)(x+2)(x+3).+1/(x+98)(x+99)(x+100)=(1/2){[1/x(x+1) - 1/(x+1)(x+2)] + [1/(x+1)(x+2) - 1/(x+2)(x+3)]+.+[1/(x+98)(x+99) - 1/(x+99)(x+100)]}=(1/2){1/x(x+1) - 1/(x+99)(x+100)}=[(x+99)(x...