This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 27

2018 VJIMC, 2
Let $n$ be a positive integer and let $a_1\le a_2 \le \dots \le a_n$ be real numbers such that \[a_1+2a_2+\dots+na_n=0.\] Prove that \[a_1[x]+a_2[2x]+\dots+a_n[nx] \ge 0\] for every real number $x$. (Here $[t]$ denotes the integer satisfying $[t] \le t<[t]+1$.)
integer part inequalities algebra floor function floor and ceiling functions mathematical induction number theory

2008 Gheorghe Vranceanu, 1
At what index the harmonic series has a fractional part of $ 1/12? $
integer part number theory fractional part floor function floor and ceiling functions fractional parts