1/1×4+1/4×7+1/7×10+.+1/2012×2015等于多少

分析
1/1×4=1/3(1-1/4)
1/4×7=1/3(1/4-1/7)
1/7×10=1/3(1/7-1/10)
………………
1/2012×2015=1/3(1/2012-1/2015)
原式
=1/3(1-1/4)+1/3(1/4-1/7)+……+1/3(1/2012-1/2015)
=1/3[(1-1/4)+(1/4-1/7)+……+(1/2012-1/2015)]
=1/3[1+(1/4-1/4)+(1/7-1/7)+……+(1/2012-1/2012)-1/2015]
=1/3(1-1/2015)
=1/3×2014/2015
=2014/6045

1/1×4+1/4×7+1/7×10+.....+1/2012×2015
=[(1-1/4)+(1/4-1/7)+(1/7-1/10)+......+(1/2012-1/2015)]/3
=(1-1/2015)/3=2014/6045

1/1×4+1/4×7+1/7×10+.....+1/2012×2015
=(1/3)(1-1/4+1/4-1/7+1/7-1/10+....+1/2012-1/2015)
=(1/3)(1-1/2015)
=(1/3)(2014/2015)
=2014/6045