### Finding the value of e

Euler’s number,

Since this is an exponential function, it should be reasonably easy to see that

But what is the value of

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

Mathematics

*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:Mathematics

Labels: mathematics, real numbers

## 5 Comments:

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

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

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

cool!

Really enjoy your math posts :-)

黄德峻:Oh yes... seems like many people think quite highly of

eand 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!

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