Quote:
Originally Posted by rudy235
I have proven heuristically that the highest number of a for which the series still converges is e^{1/e} ~ 1.44466786100977
The term a_{n} n> ∞ . is e (2.718281828...)

Assuming the limit x satisfies
we have
It is an easy exercise to prove that the largest value of
for positive real x (logarithmic differentiation works nicely) is
This occurs at