试解方程：2/(x+1)(x+2) + 2/(x+2)(x+3)＋ … ＋2/(x+10)(x+11)=5x/(x+1)(x+11)
问题描述：
试解方程：2/(x+1)(x+2) + 2/(x+2)(x+3)＋ … ＋2/(x+10)(x+11)=5x/(x+1)(x+11)
答
脑袋都想炸了。
计算：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)]
把相邻的抵消
剩下1/(x+1)-1/(x+2004)=2003/(x+1)(x+2004)
呵呵，加油 ！不懂的话再问，诚答！
答
分别把分母项化成2/(x+1)(x+2) =2{1/(x+1)-1/(x+2)},,这样前面的就都相加消去了，，，后面就是很简单了，，自己做吧
答
裂项求和
即 2(1/(x+1)-1/(x+2))+2(1/(x+2)-1/(x+3))+...2(1/(x+10)-1/(x+11))
=5x/(x+1)(x+11)
即 2*10=5x
所以 x=4