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# KCC's quizzes AQQ255 about a limit at infinite

And here is a new quiz coming!

1. Info: the frequent winners should have received some award and certificate. Please warn me if you think you have been forgotten!

2. Quote of the week: "The elevator to success is out of order. You'll have to use the stairs... one step at a time." - Joe Girard.

3. New quiz of the week: AQQ255 about a limit to infinite

Good luck!

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[edited by: emassa at 3:52 PM (GMT -4) on 21 Mar 2024]
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• (oops! I send through email rather that here.  I repost it here just for a proper way to do it)

1. e
2.  Not really rigorously mathematical, but with a numerical confirmation in Excel, that is "engineeringly" good enough. Here how it goes:

(1+a)^n      = 1 + na  + n(n-1) a^2  /2!   + n(n-1)(n-2)(n-3)  a^3  ? 3! + ... (binomial expansion)
(1+1/x)^n   = 1 + n/x  + n(n-1) x^-2  /2! +   ...   (replace a by 1/x )
(1+1/x)^x    =  1  + 1  +  x(x-1) x^-2  /  2!  +  ...  (replace n  by x )
(lim  x -> infinity) ((1+1/x)^x)  = 1 + 1 + x^2 x^-2  /2!  +  x^3 x^-3 / 3! +  ...
(  a finite constant is negligeable in front of infinity)
= e   (Taylor's serie)
• Correct answer and Excellent devleopement  ; congratulations. An other method could be to use Hospital rule.