Tryies to converge to e but since b (1.444669) is greater than the e-root of e (≈1.444667) so it diverges to infinity (For numbers that are greater than 1 diverge to infinity, but for certain values of b less than 1 it doesn't converge but does not diverge i.e. the limit doesn't exist). Actually it converges for certain values that you can check in the link to Wolfram below.
https://www.youtube.com/watch?v=elQVZLLiod4 https://mathworld.wolfram.com/PowerTower.html
