%md **Lemma 4.** _There is an $n_0 > 0$ such that $a_n < 2^n$ for all $n > n_0$._
Lemma 4. There is an n0>0n_0 > 0n0>0 such that an<2na_n < 2^nan<2n for all n>n0n > n_0n>n0.