Limes against eternity xD

[entropie]

Ok, one for you. If you already know the solution, do not spoil it. If you have found it out by yourself, you can post it via this one:

Optimath - Formeleditor f

Just have to click on "Erzeugen"(Create) and then you can right click the formula, it is an image. You can get its URL via properties and post that as an image here.

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The question is, what is the solution to:

Maybe an easy one, maybe not, Good luck tho !

 

[Colors]

? I don't see the formula anywhere on the page.??? Or am I looking for the answer?

 

[entropie]

There may be problems with the image. I downloaded it and uploaded it on imagehost.

Do you see it now ?

 

[Colors]

lim [1 + 1/n]^n ?
n-> oo

(1?)

This is cool. I used to have to type out math problems on Microsoft Word trying to find the symbols and line them up using different font sizes.

 

[entropie]

That is a good start ! But 1 isn't the result. I give you a hint, try the sentence of L'Hospital.

 

[entropie]

ok then, I see I have more fun with this than anyone, I will solve it:

 

[ygolo]

You and I would be great friends in real life entropie.

Just to add onto the point...

One can interpret what is happening is the limit of model for "growth" through compounding split over n periods.

If n=2, (1.5)^2=2.25
If n=3, (1.333...)^3= 2.370370...
If n=4, (1.25)^4=2.44140625 (and change)
.
.
.
So you can interpret e as the result instantaneous compounding done by splitting the growth into infinitely small compoundings split over infinite number of times.