- #1
bruno67
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I am looking for a bound for the following expression
S=\sum_{n=1}^N n^k e^{-an}
where a>0 and k=1, 2, 3, or 4, apart from the obvious one:
S\le \frac{n+1}{2} \sum_{n=1}^N e^{-an} = \frac{n+1}{2}<br /> \frac{1-e^{-Na}}{e^a-1}
S=\sum_{n=1}^N n^k e^{-an}
where a>0 and k=1, 2, 3, or 4, apart from the obvious one:
S\le \frac{n+1}{2} \sum_{n=1}^N e^{-an} = \frac{n+1}{2}<br /> \frac{1-e^{-Na}}{e^a-1}
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