一个分析不等式的改进

The improvement on an analytic inequality

对于一切n=1,2,…和实数x,不等式∑nk=1(-1)kksinkx≤|x|成立,这个不等式改进了被收录在多种文献[1,2]中的相关不等式.

For \%n\%=1,2,\: and an arbitrary real number \%x\%, the inequality \$∑nk=1(-1)\+kk\%sin\%kx≤|x|\$ holds. This inequality improves the corresponding inequality which was cited by a few books\.