2021 JMPSC Accuracy Problems/Problem 9
If is a strictly increasing sequence of positive integers that satisfies find .
Say we take as as an example. The first few terms of the inequality would then be: But , reaching a contradiction.
A contradiction will also be reached at some point when or when , so that must mean .
We recall the identity that is monotically increasing. Here, we have the same case, , , and so on. The answer is
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