计算1/2×4+1/4×6+1/6×8+···+1/2006×2008

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计算1/2×4+1/4×6+1/6×8+···+1/2006×2008
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计算1/2×4+1/4×6+1/6×8+···+1/2006×2008
计算1/2×4+1/4×6+1/6×8+···+1/2006×2008

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

先找规律,1/2×4=1/2 [1/2-1/4 ]=1/8,以此类推。。。
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)
=1003/4016