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तीन समांतर श्रेढियों के n पदों के योगफल ...

तीन समांतर श्रेढियों के n पदों के योगफल क्रमशः `S_(1), S_(2),S_(3)` है। यदि प्रत्येक का प्रथम पद 1 तथा उनके सार्वअंतर क्रमशः 1, 2, 3 हों, तो सिद्ध करो कि `S_(1)+S_(3)=2S_(2).`

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If S_(1),S_(2),S_(3) be respectively the sum of n,2n and 3n terms of a GP, then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1))^(2)) is equal to