Friday, October 28, 2005

Finding the value of e

Euler’s number, e, is special in many ways. The exponential function of e is particularly fascinating in that the slope of the function at any point is equal to the function value at the point.




Since this is an exponential function, it should be reasonably easy to see that
f (0) = 1
f (1) = e

But what is the value of e?


Assuming the truth of the Taylor Series expansion of a function:



If we were to substitute the exponential function into the Taylor series, and let x = 0 and Δ = 1, then:



And there it is! The value of e is the sum of all the inverses of factorials. Expanding the summation:






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5 Comments:

Blogger 黄德峻 said...

my lecturer told me, e is the prettiest thing in the world

9:11 pm, October 28, 2005  
Anonymous fred said...

OMG math!!!! in 1 week time I'm gonna go through that stupid math test....

9:57 pm, October 28, 2005  
Blogger Samm said...

Adoi, maths ah.... pening ler. = - * / enuf for me. thanks for dropping by just now.

10:14 pm, October 28, 2005  
Anonymous profmich said...

cool!

Really enjoy your math posts :-)

8:00 am, October 29, 2005  
Blogger Lao Chen said...

黄德峻:
Oh yes... seems like many people think quite highly of e and its associated relationships.

fred:
Well, do have fun! At least try to have fun :)

samm:
Hehe... some people never get tired of these stuff. Others swear never to touch maths ever again.

profmich:
Oh thats very nice. Now i know that these are read voluntarily by more than zero persons. Woo!

12:59 pm, October 29, 2005  

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