MHB Inverse laplace transform pf infinite product

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The discussion revolves around finding the inverse Laplace transform of the infinite product represented by the function g(t) = (e^(-nt)/((n-1)!)) * (e^t - 1)^(n-1). Participants suggest that the solution may be approached through mathematical induction. There is a request for assistance in proving the inverse transform. The conversation emphasizes the need for a clear method to tackle the problem. Overall, the focus is on deriving the inverse Laplace transform effectively.
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I have to do inverse laplace transform of infinite product that is shown below. Can somebody help me with that?
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$$g(t) =\dfrac{ e^{-nt}}{(n-1)!} (e^t-1)^{n-1}$$

I suspect it can be proven using induction. Have a go.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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