(1/2+2/3+3/4+...+2011/2012)*(1+1/2+2/3+...+2010/2011)-(3/2+2/3+...+2011/2012
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 20:04:47
![(1/2+2/3+3/4+...+2011/2012)*(1+1/2+2/3+...+2010/2011)-(3/2+2/3+...+2011/2012](/uploads/image/z/7202122-34-2.jpg?t=%281%2F2%2B2%2F3%2B3%2F4%2B...%2B2011%2F2012%29%2A%281%2B1%2F2%2B2%2F3%2B...%2B2010%2F2011%29-%283%2F2%2B2%2F3%2B...%2B2011%2F2012)
(1/2+2/3+3/4+...+2011/2012)*(1+1/2+2/3+...+2010/2011)-(3/2+2/3+...+2011/2012
(1/2+2/3+3/4+...+2011/2012)*(1+1/2+2/3+...+2010/2011)-(3/2+2/3+...+2011/2012
(1/2+2/3+3/4+...+2011/2012)*(1+1/2+2/3+...+2010/2011)-(3/2+2/3+...+2011/2012
设(1/2+2/3+3/4+...+2011/2012)为x,(1+1/2+2/3+...+2010/2011)为y
原式=xy-(x+1)(y-1)
=xy-y+1-xy+x
=x-y+1
=(1/2+2/3+3/4+...+2011/2012)-(1+1/2+2/3+...+2010/2011)+1
=2011/2012
)*(2/1+3/2=+2011/2010) 设2/1+3/2+4/3++2012/2011=x 2/1+3/2++2011/2010=y (2/1+3/2+4/3++2012/2011)