An Amazing Approximation to e

An amazing pandigital approximation to e that is correct to 18,457,734,525,360,901,453,873,570 decimal places is given by:

`e\approx(1+9^(−4^(6⋅7)))^(3^(2^85))`

It was discovered by Richard Sabey in 2004.

Proof:

`(1+9^(−4^(6⋅7)))^(3^(2^85))=(1+9^(−4^42))^(3^(2^85))`

`=(1+9^(−4^42))^(3^(2*2^84))`

`=(1+9^(−4^42))^(3^(2*2^84))`

`=(1+9^(−4^42))^(9^(2^(84)))`

`=(1+9^(−4^42))^(9^(4^42))`

`=(1+\frac{1}{9^(4^42)})^(9^(4^42))`

`=(1+\frac{1}{n})^n`.