Simple Question about e^(1/e)

[tommy1729]

By some incidence I just found the article:
Barrow, D. F. (1936). Infinite exponentials. Amer. math. Monthly, 43, 150–160.

He states there in Theorem 7:
The infinite exponential \( E_{i=0}^\infty (e^{1/e}+\epsilon_i) \), where \( \epsilon_i \) are all positive or 0,
(a) will converge if \( \lim_{n\to\infty} \epsilon_n n^2 < \frac{e^{1/e}}{2e} \)
(b) will diverge if \( \lim_{n\to\infty} \epsilon_n n^2 > \frac{e^{1/e}}{2e} \).

and i assume it diverges if > or < is replaced by =.

since we dont have an upper bound.