Consider the statements
(A) \(\displaystyle\lim_{n \rightarrow \infty} \left[\frac{(3n)!}{(n!)^3}\right]^{1/n} = 27\)
(B) \(\displaystyle\lim_{n \rightarrow \infty} \left[\frac{n^n}{(n + 1) (n + 2).... (n + n) }\right]^{1/n} = \frac{e}{4}\)
Then
1
(A) is true but (B) is false.
2
(A) is false but (B) is true.
3
(A) and (B) both are true.
4
Neither (A) nor (B) is true.