# Can the Squeeze Theorem be applied in this sequence?

I am finding if the sequence $$(-1)^n\frac{(n+1)!}{3n!}$$ is convergent or divergent. I want to clarify that this sequence is divergent since the Squeeze theorem cannot be applied here (because there is (n+1)! in the numerator) and when simplified, the sequence yields to {$$(-1)^n\frac{(n+1)}{3}$$}; thus, the sequence does not approach to a single value. Am I right?

• Are you sure you have $(3)(n!)$ and not $(3n)!$ in the denominator? Jun 3 '21 at 11:50
• Yes. The term in the denominator is not enclosed in a parenthesis. Jun 3 '21 at 12:00
• Correct. The sequence is unbounded, so it cannot have a limit. The series emerging by summing up the entries does not converge either. Jun 3 '21 at 12:13