Some power series consist of an infinite number of rational terms converging to an irrational limit.
Is there a series expansion /expression built on terms of powers of $\pi$ or $e$ summing up to 1 ?
If not, any proof that a such cannot exist?
Asked
Active
Viewed 27 times
1
-
3Well, one boring example is $1 = \sum_{n=1}^\infty \frac{\pi - 1}{\pi^n}$, but that equality works for any number bigger than 1. – Marc Dec 18 '15 at 11:33