If `s_1,s_2,s_3` denote the sum of n terms of 3 arithmetic series whose first terms are unity and their common difference are in H.P., Prove that `n=(2s_3s_1-s_1s_2-s_2s_3)/(s_1-2s_2+s_3)`

Explanation

To solve the problem, we need to find the value of \( n \) in terms of the sums \( s_1, s_2, \) and \( s_3 \) of three arithmetic series whose first terms are unity and whose common differences are in harmonic progression (H.P.).

### Step 1: Define the sums of the arithmetic series

The sum of the first \( n \) terms of an arithmetic series can be expressed as:
\[ s = \frac{n}{2} \left( 2a + (n-1)d \right) \]
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