1/2*4+1/4*6+1/6*8...+1/2009*2010

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1/2*4+1/4*6+1/6*8...+1/2009*2010
1/2*4+1/4*6+1/6*8...+1/2009*2010

1/2*4+1/4*6+1/6*8...+1/2009*2010
1(/2*4)+1/(4*6)+1/(6*8)...+1/(2008*2010)
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+...+1/2*(1/2008-1/2010)
=1/2*(1/2-1/4+1/4-1/6+...+1/2008-1/2010)
=1/2*(1/2-1/2010)
=251/1005

题目错了

题目错了没?最后是2008*2010吧~~?
变型为1/4*(1/1*1*2+1/2*1/3+1/3*1/4+...+1/1004*1/1005)
=1/4*(1/1-1/2+1/2-1/3+1/3-1/4+...+1/1004-1/1005)
=1/4*(1/1-1/1005)
=1/4*1004/1005
=251/1005

1/(2*4)=0.5*(1/2-1/4)
1/(4*6)=0.5*(1/4-1/6)
...........
1/(2008*2010)=0.5*(1/2008-1/2010)
原式=0.5*(1/2-1/4+1/4-1/6+............+1/2008-1/2010)
=0.5(1/2-1/2010)