1楼冬瓜爸爸
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发表于 2010-11-7 09:24
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回复 1#kellyme 的帖子
kelly, 设原式=x，则
2*X=2/1×2×3×4+2/2×3×4×5+2/3×4×5×6+2/4×5×6×7+2/5×6×7×8
=1/1×4-1/2×3 + 1/2×5-1/3×4 + 1/3×6-1/4×5 + 1/4×7-1/5×6+1/5×8-1/6×7
=1/1×4+1/2×5+1/3×6+1/4×7+1/5×8 - (1/2×3+1/3×4+...+1/6×7)
= 1/3(1/1-1/4+1/2-1/5+1/3-1/6+1/4-1/7+1/5-1/8)- (1/2-1/3+1/3-1/4+...-1/7)
= 1/3(1/1+1/2+1/3-1/6-1/7-1/8) - 5/14
下面通分，算算就出来了。.
