Could You give a poof, comment or reference for the inequality as follows:
$$\sum_{k=1}^n(-1)^k\frac{\sin kx}{k^{\alpha}} < 0$$ for all $n=1,2,3,\ldots$ and $0<x<\pi$ and $\alpha \ge 1$
- See also:
$\sum_{k=1}^n(-1)^k\frac{\sin kx}{k^{\alpha}} < 0 ?$ with $\alpha \ge 1$ and $n=1, 2,\cdots$
Đào Thanh Oai
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