数学题请给我详细过程 1/2*4+1/4*6+1/6*8+......+1/2006*2008=?
请给我详细过程 1/2*4+1/4*6+1/6*8+......+1/2006*2008=?
=1/2ï¼1/2-1/4ï¼+1/2ï¼1/4-1/6ï¼+1/2ï¼1/6-1/8ï¼+....+1/2ï¼1/2006-1/2008ï¼
=1/2*ï¼1/2-1/4+1/4-1/6+1/6-1/8+........+1/2006-1/2008ï¼
=1/2*ï¼1/2-1/2008ï¼
=1/2*1003/2008
=1003/4016
=1/2*ï¼1/2-1/4+1/4-1/6+1/6-1/8+........+1/2006-1/2008ï¼
=1/2*ï¼1/2-1/2008ï¼
=1/2*1003/2008
=1003/4016
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第1个回答 2009-07-21
=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
此类问题皆可以下列方法求解
1/A*B = 1/(B-A)*(1/A-1/B)
=1/2(1/2-1/2008)
=1003/4016
此类问题皆可以下列方法求解
1/A*B = 1/(B-A)*(1/A-1/B)
第2个回答 2009-07-21
1/2*4+1/4*6+1/6*8+......+1/2006*2008
=1/4*(1/1*2+1/2*3+...+1/1003*1004)
=1/4*[(1/1-1/2)+(1/2-1/3)+...+(1/1003-1/1004)]
=1/4*(1-1/1004)
=1003/4016
=1/4*(1/1*2+1/2*3+...+1/1003*1004)
=1/4*[(1/1-1/2)+(1/2-1/3)+...+(1/1003-1/1004)]
=1/4*(1-1/1004)
=1003/4016
第3个回答 2009-07-21
=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
裂项
=1/2(1/2-1/2008)
=1003/4016
裂项
第4个回答 2009-07-21
1/2(1/2-1/4+1/4-1/6+...+1/2006-1/2008)=1/2(1/2-1/2008)=1/2*1003/2008=1003/4016
第5个回答 2009-07-21
1/2*4+1/4*6+1/6*8+.......+1/2006*2008
=(1/2-1/4+1/4-1/6+1/6-1/8+......+1/2006-1/2008)*1/2
=1003/2008*1/2
=1003/4016
=(1/2-1/4+1/4-1/6+1/6-1/8+......+1/2006-1/2008)*1/2
=1003/2008*1/2
=1003/4016
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