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A Halloween Nightmare!

We recently realised that this simple and elegant formula, was causing trouble to many people, even supercomputers were unable to give us a step by step solution. However, it has a very short and elegant derivation.

Let us look at the proof:

It is interesting that although extremely powerful software such as Mathematica and WolframAlpha, were able to give the correct solution "e", they didn't provide us the with the steps for the solution. However, WolframAlpha was able to provide a "Halloween Nightmare" series expansion of the limit without giving us more detailed information.

The expansion itself needs more work, in order to reach the solution: "e".

Problem: Derive "e" from the above equation. Write your comments below.


Calculations involving limits are rarely used in Physics, today. However summations: Σ, are widely used in all areas of Physics. Hence, many people with an education focused in Physics and Astronomy are often confronted with a "nightmare" when they look at a limit calculation like this. It is just that they have forgotten the identities because they rarely use limits. Limits, are so commonly seen in purely mathematical books, because they have a complexity, but this complexity doesn't really apply to problems of the real Universe, and quite often simpler alternative expressions are used in Physics textbooks.

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