The problem involves finding the smallest integer n such that the product \(5 (32 + 22)(34 + 24)(38 + 28)...(32n + 22n) > 9256\). This falls under the subject area of inequalities and products in mathematics, particularly in the context of competitive mathematics such as math olympiads.
The discussion is ongoing, with participants exploring different interpretations of the problem and sharing insights. Some guidance has been offered regarding the application of inequalities and the need for closed forms, but there is no explicit consensus on the final approach or solution.
Participants note constraints such as the need to find a lower bound for the product and the implications of discarding certain terms. There is also mention of conflicting information regarding the correct value of n, with some sources suggesting different answers.
oh you careless me but i am still getting a different result this is my workingharuspex said:That n is not the same as the n in the problem.
You are not applying the upper bound correctly in the sum. If the sum is up to the term rk then the numerator should have 1-rk+1. You omitted the +1.vishnu 73 said:now what am i doing wrong
Yes.vishnu 73 said:oh wait the index starts at i=0 not 1 so it must be 22n+1 correct ?
then it is equal to
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3^{2^{n+1}} - 2^{2^{n+1}}
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