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2*4/1+4*6/1+6*8/1......2006*2008/1

1/2*4=(1/2-1/4)/2 1/4*6=(1/4-1/6)/2 1/6*8=(1/6-1/8)/2 …… 1/2006*2008=(1/2006-1/2008)/2 所以, 原式=(1/2-1/4+1/4-1/6+1/6-1/8+…+1/2006-1/2008)/2 =(1/2-1/2008)/2=1003/4016

2×4/1+4×6/1+6×8/1+……+2006×2008/1 =2/1×(2×4/2+4×6/2+6×8/2+……+2004×2006/2+2006×2008/2) =2/1×[(2/1-4/1)+(4/1-6/1)+(6/1-8/1)+……+(2004/1-2006/1)+(2006/1-2008/1)] =2/1×(2/1-4/1+4/1-6/1+6/1-8/1+……2004/1-2006/1+2006/1-2008/1) =2/1×(2/1...

1/2×4+1/4×6+1/6×8+…1/2006×2008 =1/2×(1/2-1/4+1/4-1/6+1/6-1/8+…1/2006-1/2008) =1/2×(1/2-1/2008) =1003/4016

1/(2×4)=1/2(1/2-1/4) 1/(4×6)=1/2(1/4-1/6) 1/(6×8)=1/2(1/6-1/8) …… 1/(2006×2008)=1/2(1/2006-1/2008) 所以 原式=1/2[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+……+(1/2006-1/2008)]=1/2(1/2-1/2008)=1003/4016 这种解法称为裂项相消法。特点是分母两个...

2×4/1+4×6/1+6×8/1....+2006×2008/1 =(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2006-1/2008)÷2 =(1/2-1/2008)÷2 =1003/2008÷2 =1003/4016

2×4分之1+4×6分之1+6×8分之1+……+2006×2008分之1=1/2(1/2-1/4)+1/2(1/4-1/6)+....1/2(1/2006-1/2008)=1/2(1/2-1/2008)=1003/4016

=4016分之1003

可以用拆分法,如,1/2*4=1/2(1/2-1/4),其他的类似, 所以原式=1/2(1/2-1/4+1/4-1/6+……+1/2004-1/2006+1/2006-1/2008)=1/2(1/2-1/2008)=1/2(1003/2008)=1003/4016

1/2×4+1/4×6+1/6×8+···+1/2006×2008 =1/2×(1/2-1/4+1/4-1/6+1/6-1/8+···+1/2006-1/2008) =1/2×(1/2-1/2008) =1003/8032

1/2*4+1/4*6+1/6*8+....+1/2006*2008 =1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+....+1/2*(1/2006-1/2008) =1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2006-1/2008) =1/2*(1/2-1/2008) =1/2*(1004/2008-1/2008) =1/2*1003/2008 =1003/4016

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