Let $(a_n{)}_n=1^{}$ be a sequence starting at $n=1.$ Thus, $(a_{n-1}{)}_n=2^{}$ is a sequence starting at $n=2($which is a claim you do not need to justify$).$ If $\underset{n}{lim}{a}_n$ exists, does $\underset{n}{lim}{a}_{n-1}$ exist? If $\underset{n}{lim}{a}_n$ does not exist, does $\underset{n}{lim}{a}_{n-1}$ exist? If the limits exists, how are they related?

Part of this problem is to clearly formulate your claims. You must justify your claims with proofs using the formal $in-N$ definition of a limit$.$