Problem: If P is the product of n quantities in Geometric Progression, S their sum, and S′ the sum of their reciprocals, then P in terms of S,S′, and n is
Answer Choices:
A. (SS′)21n
B. (S/S′)21n
C. (SS′)n−2
D. (S/S′)n
E. (S′/S)21(n−1)
Solution:
Let the progression be a,ar,ar2,⋯arn−1, then P=anr21(n−1)n,S=a1−r1−rn, S′=a1⋅1−r−11−r−n=ar−(n−1)⋅1−r1−rn∴S/S′=a2r(n−1)∴(S/S′)21n=anr21(n−1)n=P.