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(1/4×1/6+1/6×1/8+1/8×1/10+1/10×1/12)×2简便解法
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(1/4×1/6+1/6×1/8+1/8×1/10+1/10×1/12)×2简便解法
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答案和解析
先知道一个拆项的技巧:1/n×1/(n+2)=1/2×[1/n-1/(n+2)]
用上面的拆项等式来化简题目:
(1/4×1/6+1/6×1/8+1/8×1/10+1/10×1/12)×2
=1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12
=1/4-1/12
=1/6
用上面的拆项等式来化简题目:
(1/4×1/6+1/6×1/8+1/8×1/10+1/10×1/12)×2
=1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12
=1/4-1/12
=1/6
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