I need to show that for f(t)=f(t+T) on [0,infty), that the Laplace Transform is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mathcal{L}\left[f(t)\right]=\frac{\int_0^Te^{-st}f(t)\,dt}{1-e^{-sT}}.[/tex]

The first thing I did was to write the transform as:

[tex]\mathcal{L}\left[f(t)\right]=\sum_{n=0}^{\infty}\int_{nT}^{\left(n+1\right)T}e^{-st}f(t)\,dt.[/tex]

Am I on the right track here? It looks like the formula given to me (that I need to show) is an infinite geometric series multiplied by the integral in the numerator. However, I am unable to get what I have into something of that form. Any ideas?

Thank you.

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# Homework Help: Laplace Transform Question

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