Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 9"
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+ | ==Solution 2== | ||
+ | We recall the identity that <math>\frac{x}{x+1}</math> is monotically increasing. Here, we have the same case, <math>x_1=3</math>, <math>x_2=4</math>, and so on. The answer is <math>\frac{12(13)}{2}-3=\boxed{75}</math> | ||
+ | |||
+ | ~Geometry285 | ||
+ | |||
+ | ==See also== | ||
+ | #[[2021 JMPSC Accuracy Problems|Other 2021 JMPSC Accuracy Problems]] | ||
+ | #[[2021 JMPSC Accuracy Answer Key|2021 JMPSC Accuracy Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Latest revision as of 17:24, 11 July 2021
Contents
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.