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

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

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*1003/2008
=1003/4016

=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(1/2-1/4+1/4-1/6+...+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
=1/4*(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

=1/2(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*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

|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006| 1/2+1/4+1/6+1/8+.1/n 1+6+6+8+4+2+6+6+5+4+4+1+4+7+45 1+1/2+4+1/2+4+6+1/2+4+6+8+.+1/2+4+6+8...+20 1/2*4+1/4*6+1/6*8+1/8*10+---+1/198*200 10,1,8,1,6,2,4,6,2,（）. 1/2*4*6+1/4*6*8+1/6*8*10+.+96*98*100 1/2*4+1/4*6+1/6*8+.+1/2006*2008=(1/2*4)+(1/4*6)+(1/6*8)+..........+(1/2006*2008) 1/2*4+1/4*6+1/6*8+1/8*10.1/2006*2008 计算1/2*4+1/4*6+1/6*8+.+1/2002*2004+1/2004*2006 1+1+2+1+2+6+4+5+8等于 1/4+5/8+6/2=? 1,2,3,4,5,6,8 1×2×3×4×5×6×8 2/1+4/1+4/1+6/1+8/1+16/1+32/1=? 1,2,4,6, [2^4+1/4)(4^4+1/4)(6^4+1/4)(8^4+1/4)(10^4+1/4)】/[1^4+1/4)(3^4+1/4)(5^4+1/4)(7^4+1/4)(9^4+1/4)] 2+2+5+0+4+1+6+8+2+6