Alg8.21

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Insert 4 harmonic means between \frac{1}{12}\, and \frac{1}{42}\,

Let the harmonic means be \frac{1}{a+d},\frac{1}{a+2d},\frac{1}{a+3d},\frac{1}{a+4d}\,

The first term is \frac{1}{a}=\frac{1}{12},a=12\,

The last term is \frac{1}{a+5d}=\frac{1}{42},a+5d=42,5d=30,d=6\,

Therefore,the harmonic means are \frac{1}{12+6},\frac{1}{12+12},\frac{1}{12+18},\frac{1}{12+24}\,

\frac{1}{18},\frac{1}{24},\frac{1}{30},\frac{1}{36}\,


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