Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 9"
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+ | Say we take <math>x_1,x_1,x_3,...,x_{10}</math> as <math>4,5,6,...,13</math> as an example. The first few terms of the inequality would then be: | ||
+ | <cmath>\frac{1}{2}<\frac{2}{4}<\frac{3}{5}<\frac{4}{6}</cmath> | ||
+ | But <math>\frac{3}{5}<\frac{4}{6}</math>, reaching a contradiction. | ||
+ | |||
+ | A contradiction will also be reached at some point when <math>x_1\geq 4</math> or when <math>x_1\leq 2</math>, so that must mean <math>x_1=3</math>. | ||
+ | |||
+ | <math>\implies 3+4+5+...+12=\frac{10\cdot 15}{2}=\boxed{75}</math> | ||
+ | <math>\linebreak</math> | ||
+ | ~Apple321 |
Revision as of 11:12, 11 July 2021
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