Prove or disprove if the sequence {x_n^8} converges, then the sequence {x_n} also converges.

Question

Prove or disprove:

If the sequence $\{x_n^8\}$ converges, then the sequence $\{x_n\}$ also converges.

Trying to find a way to prove this without using a direct proof to avoid using cases; but then got stuck trying to define $\{x_n\}$ as a subset of $\{x_n^8\}$.

Answer 1

Hint: Try $x_n=(-1)^n$. $ \ \ \ \ \ \ \ \ \ $