Euler's number e and Jacob Bernoulli's expression

[JeremyEbert]

Jacob Bernoulli's expression for e:

n-> LIM (1+1/n)^n

converges much slower than

n-> LIM (n-1/n+1)^(-2/n)

is this a better expression for e?

edit!
n-> LIM (n-1/n+1)^(-n/2)
sorry for the typo!

 

[dextercioby]

For the record, any sequence of numbers converging to the same limit as (1+(1/n))^n could be taken as a definition of "e".

 

[JeremyEbert]

yea, I know there are a good amount of equations converging around e.
n-> LIM (n-1/n+1)^(-n/2) just seems to do it quickly and its a core piece to and equation I've been working on.