Graham's Number

[Jorge]

Play nice! At least in this thread, understand?

I was "playing nice". Geesh - no sense of humor.

Besides, what I wrote is true, ask anyone.

Jorge

[Juvenal]

Now, d(arctan(x))/dx = 1/(1+x^2) = 1 - x^2 + x^4 - x^6 + ...
so arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
hence arctan(1) = 1 - 1/3 + 1/5 - 1/7 + ...
so, since tan(pi/4) = 1 and thus arctan(1) = pi/4 ...

pi = 4 - 4/3 + 4/5 - 4/7 + ...

Since the least common multiple of the denominators must include every prime, and there is no largest prime, pi not only has no last digit, but is irrational.

(In fact, it's transcendental.)