The following method of computing π is due to Archimedes: Write a program to implement the algorithm. The transcendental number e XXXXXXXXXX ...) can be shown to be the limit of (1 + x) 1/x as x tends...

The following method of computing π is due to Archimedes:

Write a program to implement the algorithm.

The transcendental number e (2.71828182845904 ...) can be shown to be the limit of

(1 + x)^1/x

as x tends to zero (from above). Write a program which shows how this expression converges to e as x gets closer and closer to zero.