Question

解方程：x/1×2+x/2×3+x/3×4+……+x/2008×2009=2008

Answer 1

解 ；因为x/1×2+x/2×3+x/3×4+……+x/2008×2009
=x(1/1×2+1/2×3+1/3×4+……+1/2008×2009)
=x(1-1/2+1/2-1/3+1/3-1/4+………+1/2008-1/2009)
=x(1-1/2009)
=x2008/2009=2008
所以 x=2009

Answer 2

x/1×2=x/1-x/2
同理其他的都是可以化作这个形式；所以原式等价于：x/1-x/2009=2008x/2009

Answer 3

x（1-1/2+1/2-1/3+1/3-1/4+…………+1/2008-1/2009）=2008
x（1-1/2009）=2008
2008x/2009=2008
x=2009

Answer 4

原式=X(1-1/2+1/2-1/3+1/3-1/4......1/2008-1/2009)=2008X/2009

Answer 5

x(1-1/2+1/2-1/3+……+1/2008-1/2009)=2008
x*2008/2009=2008
x/2009=1
x=2009