一道能用简便方法的计算题.[1-(1/2)-(1/3)-...-(1/2008)]×[(1/2)+(1/3)+(1/4)+...+(1/2009)]-[1-(1/2)-(1/3)-...-(1/2009)]×[(1/2)+(1/3)+(1/4)+...+(1/2008)]

一道能用简便方法的计算题.[1-(1/2)-(1/3)-...-(1/2008)]×[(1/2)+(1/3)+(1/4)+...+(1/2009)]-[1-(1/2)-(1/3)-...-(1/2009)]×[(1/2)+(1/3)+(1/4)+...+(1/2008)]
一道能用简便方法的计算题.
[1-(1/2)-(1/3)-...-(1/2008)]×[(1/2)+(1/3)+(1/4)+...+(1/2009)]-[1-(1/2)-(1/3)-...-(1/2009)]×[(1/2)+(1/3)+(1/4)+...+(1/2008)]

一道能用简便方法的计算题.[1-(1/2)-(1/3)-...-(1/2008)]×[(1/2)+(1/3)+(1/4)+...+(1/2009)]-[1-(1/2)-(1/3)-...-(1/2009)]×[(1/2)+(1/3)+(1/4)+...+(1/2008)]
1/2009
令x=1-(1/2)-(1/3)-...-(1/2008） y=（1/2)+(1/3)+(1/4)+...+(1/2008）
所以原式=x（y+1/2009）-（x-1/2009）y=（x+y）/2009
x+y=1-(1/2)-(1/3)-...-(1/2008）+（1/2)+(1/3)+(1/4)+...+(1/2008）=1
所以原式=1/2009