Inequality
Source: Vietnam NMO 1989 Problem 1
February 1, 2009
inequalitiestrigonometryinequalities unsolved
Problem Statement
Let and be natural number. Prove that for any , , and any real , it holds that { |\sum_ {k=0}^n}\frac{\sin((\alpha+k)x)}{N+k}|\le\min\{(n+1)|x|, \frac{1}{N|\sin\frac{x}{2}|}\}