2. Let (an)2 1 be a sequence with positive terms, such that lim an+1 = 2023. Show that lim an = 00. an Hints: Recall that lim On = L, when for every & > 0 there exists an integer N such that I-E N. Use this definition to show that there exists an integer N such that ant1 2 an for all n > N. - Suppose that (an) , is bounded above. Can you then conclude something about its limit? - Apply the Algebraic Limit Theorem to anti . ] an