Let S , P , R be the sum, product, and sum of reciprocals of the n nonzero terms of an increasing G.P. If S n = R n P k and P  = 1 , find k for nontrivial positive terms.

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For terms a , a r , … , a r n − 1 , pairing t i ​ with t n + 1 − i ​ gives a common product a 2 r n − 1 = P 2/ n . Hence S / R = P 2/ n , and raising to n gives S n / R n = P 2 ; therefore k = 2 .

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