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Infinite-Math-Power-Function

Recently I have been solving some limit problems and came across this problem:

now as you can see if you are a math geek it's easy enough to solve I also came to know that this is a thing:

So I was wondering if it is possible that if a computer will compute some function like that will the output be same or something different to I create the program but it ends up hanging my pc for like 10-15 mins and then memory error came up then i decided to give some limit to the function to it can stop but still the same thing happend but this time after things become normal I had a memory error. So I was wondering if there is a way to solve such problems using a piece of code cause directly doing math doesn't seem like a good idea.

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Simple math function

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