Proof of (1+1/n)^n=e

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Why the limit of (1+1/n)^n as n approaches infinity is e?
Prove by using Binomial Theorem.

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Proof of the limit of (1+1/n)^n = e using:

Proof of the derivative of ln x using:

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If have to prove more than one case at once. Here are some combinations.

limit of (1+1/n)^n = e and d/dx(lnx) = x
or
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Finally a non-circular proof that doesn't rely on natural logarithms -- thank you!

lapsecontinuum
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please create video and tell us why sum of 1/n! is equal to e??

Humanity
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Thank you, how to prove that series expansion of 1/n factorial is equal to e?

jameyatesmauriat
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Eh, as far as I know binomial theorem is using a permutation and a combination, not a Taylor series....
[Good video, anyway.]

FaranAiki
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Exactly what i was trying to do for the last 2 days. Thanks.

fhdxbdh
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very nice proof without circular reasoning finally

AdoptedPoo
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Can you prove that (1+1/n)^n < e for any natural n by mathematical induction(without using this limit), please?

michaelsondei
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If n is natural then how can this expansion be infinite ?

RigorousMathematicsByProfUsman
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Can you please solve the same problem with

Classwork
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This wasn't the proof that I was looking for, but I'm glad I stuck through the whole thing. Thanks for sharing

ignantxxxninja