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 that \((m+n)\left(\frac{1}{m}-\frac{1}{p}\right)=(m+p)\left(\frac{1}{m}-\frac{1}{n}\right)\), we start by using the properties of the arithmetic progression (A.P.).

### Step-by-Step Solution:

1. **Understanding the Sum of Terms in A.P.:**
The sum of the first \(m\) terms of an A.P. can be expressed as:
\[
S_m = \frac{m}{2} \left(2a + (m-1)d\right)
...