CMIMC 2020 Power Problem 5.1

Alice wants to send Bob n messages, all of the same length. When Bob’s received the n messages, he will send her a special passage in response. Unfortunately, Alice has no way to know whether her messages reach Bob, so they have to adopt a clever strategy to ensure the expected number of messages Alice must send is small.
One strategy would be for Alice to send all n messages one after another, then wait to see whether Bob has received them all, and send them all again if not. Bob will keep every message he receives until he has eventually received all of them. Show that, for sufficiently large n, the expected number of messages Alice sends is more than 10n.