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## Main Question or Discussion Point

I am looking for a bound for the following expression

[tex]S=\sum_{n=1}^N n^k e^{-an}[/tex]

where a>0 and k=1, 2, 3, or 4, apart from the obvious one:

[tex]S\le \frac{n+1}{2} \sum_{n=1}^N e^{-an} = \frac{n+1}{2}

\frac{1-e^{-Na}}{e^a-1}[/tex]

[tex]S=\sum_{n=1}^N n^k e^{-an}[/tex]

where a>0 and k=1, 2, 3, or 4, apart from the obvious one:

[tex]S\le \frac{n+1}{2} \sum_{n=1}^N e^{-an} = \frac{n+1}{2}

\frac{1-e^{-Na}}{e^a-1}[/tex]

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