Prove that if $\{a_n\}$ converges to $a$ and $|a| < 1$, then $\{(a_n)^n\}$ converges to 0.
This is what I have currently done. Please let me know if there is something wrong or if there is any other advice that you could provide to help me finish this.
Suppose $\{a_n\}$ converges to $a$ and $|a| < 1$. Since $\{a_n\}$ converges, then we know that $\{a_n\}$ is bounded. So there exists $M$ such that $|a_n| \leq M$. Then $-M \leq a_n \leq M$ for all $n$.
So I guess the problem that I am having is how to get M to be equal to 1. Thanks in advance.