(1/2+1/3+"""+1/2008)*(1+1/2+1/3+'''''+1/2007)-(1+1/2+1/3+''''+1/2008)*(1/2+1/3+'''''1/2007)1/2指二分之一,1/3,指三分之一,1/2008指二零零八分之一,1/2007指二零零七分之一看,''''''''''指省略,一直加到1/2008或1/2007.

Question

(1/2+1/3+"""+1/2008)*(1+1/2+1/3+'''''+1/2007)-(1+1/2+1/3+''''+1/2008)*(1/2+1/3+'''''1/2007)
1/2指二分之一,1/3,指三分之一,1/2008 指二零零八分之一,1/2007指二零零七分之一看,''''''''''指省略,一直加到1/2008或1/2007.

Answer 1

设1/2+1/3+……+1/2008=x
1/2+1/3+……+1/2007=y
(1/2+1/3+"""+1/2008)*(1+1/2+1/3+'''''+1/2007)-(1+1/2+1/3+''''+1/2008)*(1/2+1/3+'''''1/2007)
=x*(1+y)-(1+x)*y
=x+xy-y-xy
=x-y
=1/2008