Insert 6 harmonic means between 3 and `(6)/(23)`

Explanation

To insert 6 harmonic means between 3 and \( \frac{6}{23} \), we can follow these steps:

### Step 1: Understand the relationship between Harmonic Means and Arithmetic Progression (AP)
If we have two numbers \( a \) and \( b \), the harmonic means between them can be found by taking the reciprocals of these numbers and forming an arithmetic progression (AP) with those reciprocals.

### Step 2: Set up the problem
Let the harmonic means be \( h_1, h_2, h_3, h_4, h_5, h_6 \). We have:
- First term \( a = 3 \)
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