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 given problem step by step, we need to find the arithmetic means (A.M.) and harmonic means (H.M.) inserted between the numbers 2 and 3, and then prove that \( A + \frac{6}{H} = 5 \).

### Step 1: Finding the Common Difference of A.M.
We know that 9 arithmetic means are inserted between 2 and 3. This means we have a total of 11 terms in an arithmetic progression (A.P.):

- First term \( a = 2 \)
- Last term \( a_{11} = 3 \)

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