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)]
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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