If the sum of `m` terms of an A.P. is equal to the sum of either the next `n` terms or the next `p` terms, then prove that `(m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot`

Explanation

To prove the statement given in the question, we will follow a systematic approach using the properties of Arithmetic Progressions (AP).

### Step-by-Step Solution:

1. **Understanding the Sums of Terms in an A.P.**:
The sum of the first `m` terms of an A.P. can be given by the formula:
\[
S_m = \frac{m}{2} \times (2a + (m-1)d)
...