If the common ratio of a geometric progression is positive, find the maximum of the ratio of its second term to the sum of its first three terms.

Question

TestHub · Accepted Answer

For terms a / r , a , a r , the ratio is 1/ ( r + 1 + 1/ r ) . Since r + 1/ r ≥ 2 for r > 0 , the denominator is at least 3, and the maximum is 1/3.

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