If nine arithmetic means and nine harmonic means are inserted between 2 and 3 alternatively, then prove that `A+6//H=5` (where `A` is any of the A.M.'s and `H` the corresponding H.M.)`dot`

Explanation

To solve the problem of finding the relationship between the arithmetic means (A) and harmonic means (H) inserted between 2 and 3, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Terms**:
We have 9 arithmetic means (A.M.s) and 9 harmonic means (H.M.s) inserted between the numbers 2 and 3. This gives us a total of 11 terms (2, A1, A2, ..., A9, H1, H2, ..., H9, 3).

2. **Find the Common Difference for A.M.s**:
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