1/2*4+1/4*6+1/6*8+…+1/2010*2012等于什么?

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1/2*4+1/4*6+1/6*8+…+1/2010*2012等于什么?

1/2*4+1/4*6+1/6*8+…+1/2010*2012等于什么?
1/2*4+1/4*6+1/6*8+…+1/2010*2012等于什么?

1/2*4+1/4*6+1/6*8+…+1/2010*2012等于什么?
1/2*4+1/4*6+1/6*8+…+1/2010*2012
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1005/4024

1/2*4+1/4*6+1/6*8+…+1/2010*2012
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1005/4024

1/2*4+1/4*6+1/6*8+…+1/2010*2012
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1005/4024

1/2*4+1/4*6+1/6*8+…+1/2010*2012
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1/2*1005/2012
=1005/2024

1/2*4+1/4*6+1/6*8+…+1/2010*2012
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1005/4024

1/2*4+1/4*6+1/6*8+…+1/2010*2012
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1005/4024


原式=1/2 * (1/2-1/4+1/4-1/6+……-1/1012)
=1/2 * 1005/2012
=1005/4024

1/2*[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(1005*1006)]=1/2*[(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/1005-1/1006)]=1/2*[1-1/1006]=1/2*(1005/1006)=1005/2012