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If the sum of the first \( m \) terms of an A.P. is equal to the sum of either the next \( n \) terms or the next \( p \) terms, then prove that \( (m+n)\left(\frac{1}{m}-\frac{1}{p}\right)=(m+p)\left(\frac{1}{m}-\frac{1}{n}\right) \).
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