Let $\mathrm{S}_{\mathrm{n}}=\sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{\mathrm{n}}{\mathrm{n}^2+\mathrm{kn}+\mathrm{k}^2}$ and $\mathrm{T}_{\mathrm{n}}=\sum_{\mathrm{k}=0}^{\mathrm{n}-1} \frac{\mathrm{n}}{\mathrm{n}^2+\mathrm{kn}+\mathrm{k}^2}$ for $\mathrm{n}=1,2,3, \ldots$. Then,
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