杭州交通信息网小女孩衣服品牌有哪些:初一数学
来源：百度文库 编辑：杭州交通信息网 时间：2024/04/28 20:51:18
1/(X+1)(X+2)+1/(X+2)(X+3)+1/(X+3)(X+4)+.......+1/(X+2003)(X+2004)
1/(X+1)(X+2)+1/(X+2)(X+3)+1/(X+3)(X+4)+.......+1/(X+2003)(X+2004)
=[1/(x+1) - 1/(x+2)] + [1/(x+2) - 1/(x+3)] + [1/(x+3) - 1/(x+4) + ………… + [1/(x+2003) - 1/(x+2004)]
= 1/(x+1) - 1/(x+2004)
= 2003/(x+1)(x+2004)
因为 1/(x+n)(x+n+1)=1/(x+n)-1/(x+n+1)
所以原式= 1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+......+1/(x+2003)-1/(x+2004)=1/(x+1)-1/(x+2004)=2003/(x+1)(x+2004)
原式=[1/（x+1）-1/（x+2）]+[1/（x+2）-1/（x+3）]+[1/（x+3）-1/（x+4）]+......+[1/(x+2003)-1/(x+2004)]=1/(x+1)-1/(x+2004)=2003/(x+1)(x+2004)