For which values of t 1 does the expression t^t^t^t . . . make sense? (a) Show that an+1 an for all n 1. What does this tell you?

For which values of t > 1 does the expression t^t^t^t . . . make sense?

(a) Show that an+1 > an for all n ≥ 1. What does this tell you?

(b) When L = limn→∞ an exists, solve for t in terms of L. Use this to find the optimal upper bound for those values of t for which the limit exists. What happens for larger t?

(c) For these values of t, show by induction that an is bounded above by e for all n ≥ 1. What does this tell you?