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# why does lim n->infinity (1+1/n)^n=e

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why does lim n->infinity (1+1/n)^n=e

Guest Mar 18, 2015

#1
+92254
+10

This is a good question.

$$\displaystyle\lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^n=2.718281828.....\qquad=e\\$$

This limit is used all the time (for continual compounding) so it was decided to give this number a formal symbol, that symbol is e

e is called Euler's number after the Swiss mathematician Euler,  it is also called the Napier constant.

Here is the graph to show you

https://www.desmos.com/calculator/fa8qrqn33u

To derive e requires higher mathematics but here are some related web pages.      ヽ(^o^)ノ

http://en.wikipedia.org/wiki/E_%28mathematical_constant%29

http://www.dsprelated.com/showmessage/68565/1.php

Melody  Mar 19, 2015
Sort:

#1
+92254
+10

This is a good question.

$$\displaystyle\lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^n=2.718281828.....\qquad=e\\$$

This limit is used all the time (for continual compounding) so it was decided to give this number a formal symbol, that symbol is e

e is called Euler's number after the Swiss mathematician Euler,  it is also called the Napier constant.

Here is the graph to show you

https://www.desmos.com/calculator/fa8qrqn33u

To derive e requires higher mathematics but here are some related web pages.      ヽ(^o^)ノ

http://en.wikipedia.org/wiki/E_%28mathematical_constant%29

http://www.dsprelated.com/showmessage/68565/1.php

Melody  Mar 19, 2015
#2
0

is it acually possible to derive e? isnt it just a number?

can you explain the number e in words? like pi would be describe as the perimeter of a circkle if the diameter is 1 but what would you say about e?

Guest Mar 22, 2015
#3
+92254
+5

This is the description of what e is

$$\displaystyle\lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^n=2.718281828.....\qquad=e\\$$

it just doesn't make much sense to you yet. :))

Melody  Mar 23, 2015

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