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I am reading some material that using mathematics extensively, and I encountered with the following result:

[tex]\frac{N}{\overline{\gamma}}\,\int_0^{\infty}\gamma\,\left[1-\mbox{e}^{-\gamma/\overline{\gamma}}\right]^{N-1}\,\mbox{e}^{-\gamma/\overline{\gamma}}\,d\gamma=\,\overline{\gamma}\sum_{k=1}^N\frac{1}{k}[/tex]

How did they get there? I tried to use the binomial expansion and assemble the exponentials, but the result was totally different. Any hint will be highly appreciated.

Thanks in advance

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# How to obtain this?

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