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Difference between revisions of "1973 IMO Problems/Problem 6"

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==Solution==
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The discussion thread for this problem is here: [https://aops.com/community/p357934]
 
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Revision as of 14:52, 29 January 2021

Problem

Let $a_1, a_2,\cdots, a_n$ be $n$ positive numbers, and let $q$ be a given real number such that $0<q<1.$ Find $n$ numbers $b_1, b_2, \cdots, b_n$ for which

(a) $a_k<b_k$ for $k=1,2,\cdots, n,$

(b) $q<\dfrac{b_{k+1}}{b_k}<\dfrac{1}{q}$ for $k=1,2,\cdots,n-1,$

(c) $b_1+b_2+\cdots+b_n<\dfrac{1+q}{1-q}(a_1+a_2+\cdots+a_n).$

Solution

The discussion thread for this problem is here: [1] This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

1973 IMO (Problems) • Resources
Preceded by
Problem 5 		1 • 2 • 3 • 4 • 5 • 6 Followed by
Last Question
All IMO Problems and Solutions
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