Consider the sequence t0 = 3, t1 = 3^3, t2 = (3^3)^3, t3 = ((3^3)^3)^3 , . . . defined by t0 = 3 and tn+1 = 3tn for n > 0.

What are the last two digits in t3 = ((3^3)^3)^3? Can you say what the

last three digits are? Show that the last 10 digits of tk are the same for all k > 10.