Find all $x$ for which, for all $n,$ \[\sum^n_{k=1} \sin {k x} \leq \frac{\sqrt{3}}{2}.\]
Problem
Source: IMO LongList 1967, Soviet Union 3
Tags: trigonometry, Trigonometric inequality, Inequality, algebra, IMO Shortlist, IMO Longlist
Source: IMO LongList 1967, Soviet Union 3
Tags: trigonometry, Trigonometric inequality, Inequality, algebra, IMO Shortlist, IMO Longlist
Find all $x$ for which, for all $n,$ \[\sum^n_{k=1} \sin {k x} \leq \frac{\sqrt{3}}{2}.\]