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If $a>b>0$ and $\alpha = \frac{x+1}{2y}$ where $y>0$ and $x\geq 0$. Under which conditions the following summation is asymptotically ($n\to \infty$) upper-bounded by $ k n$ where $k$ is a positive finite constant.

$$ e^{ \alpha \log{( \frac{a}{b})} \log(n)} \times \sum_{t=1}^{n/2} e^ {- \frac{2t}{3} (\log(t) - 3) }$$

Thank you all for your assistance in advance.

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