题目

The harmonic mean of n numbers is the reciprocal of the arithmetic mean of their reciprocals. What is the harmonic mean of 2, 4, 6, and 12 ?

选项

A.

B.

C.

1

D.

4

E.

6

解析

求\(\left( \frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{12} \right)\)的算术平均数 分母的最小公倍数(LCM)= 12 平均数 = 总和 ÷ 项数 总和 = \(\frac{6+3+2+1}{12} = \frac{12}{12} = 1\) 算术平均数 = \(\frac{1}{4}\) 调和平均数 = \(1 \div (\frac{1}{4}) = 4\) 选项D
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