Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 9"
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+ | ==See also== | ||
+ | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||
+ | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Revision as of 16:20, 11 July 2021
Contents
[hide]Problem
If is a strictly increasing sequence of positive integers that satisfies find .
Solution
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 .
~Apple321
Solution 2
We recall the identity that is monotically increasing. Here, we have the same case, , , and so on. The answer is
~Geometry285
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.