if the sum of the first m terms of m AP is the same as the sum of its first n terms, show that the sum of its first (m+n) terms is zero.
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In this question, it is given that the sum of m terms of an A.P. is the same as the sum of its n terms and we have to show that the sum of its (m + n) terms is zero. Hence, we have proved that the sum of (m + n) terms of this A.P. is zero. Note: In the equation (4), we can cancel the factor (m - n) only when m−n≠0.
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