1/6+1/12+1/20+1/30+...=1/2005*2006
问题描述：
1/6+1/12+1/20+1/30+...=1/2005*2006
答
1/6+1/12+1/20+1/30+.......+1/2005*2006=
=[1/(2*3)]+[1/(3*4)]+[1/(4*5)]+[1/(5*6)]+……+[1/(2005*2006)]
=(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+(1/5)-(1/6)+……+(1/2005)-(1/2006)
=(1/2)-(1/2006)
=1002/2006
=501/1003
以上回答你满意么？
答
原式
=1/2x3+1/3x4+1/4x5+……+1/2005x2006
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2005-1/2006
=1/2-1/2006
=1003/2006-1/2006
=1002/2006
=501/1003