This is LaTeX code:

[latex]
x_k := (-1)^{2k-1}\frac{a_{2k-1}}{2k-1} + (-1)^{2k}\frac{a_{2k}}{2k} = \frac9{2k}-\frac1{2k-1} > \frac8{2k} = \frac4k
[/latex]