1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+…+1/(x+2001)(x+2002)=(2x+4001)/(3x+6006)
问题描述:
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+…+1/(x+2001)(x+2002)=(2x+4001)/(3x+6006)
答
化简,得:2001/[(x+1)(x+2002)]=(2x+4001)/[3(x+2002)]; 两边同乘:3(x+1)(x+2002); 得2011x+2011=6x+12003 化简:2005x=10992 x=10992/2005