1/2+1/6+1/12+1/20……+1/2008*2009快哟!急用!
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![1/2+1/6+1/12+1/20……+1/2008*2009快哟!急用!](/uploads/image/z/7133510-38-0.jpg?t=1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%E2%80%A6%E2%80%A6%2B1%2F2008%2A2009%E5%BF%AB%E5%93%9F%21%E6%80%A5%E7%94%A8%21)
1/2+1/6+1/12+1/20……+1/2008*2009快哟!急用!
1/2+1/6+1/12+1/20……+1/2008*2009
快哟!急用!
1/2+1/6+1/12+1/20……+1/2008*2009快哟!急用!
一般地,易证1/n(n-1)=1/(n-1)-1/n ,那么 ,原式=1/2+(1/2-1/3)+(1/3-1/4)+……+(1/2008-1/2009)=1-1/2009=2008/2009