If is a sequence of real numbers such that , then
(A) is a bounded sequence
(B) is an unbounded sequence
(C) is a convergent sequence
(D) is a monotonically decreasing sequence
If was bounded, show that , by sandwich theorem.
If was convergent, show that , by algebra of limits.
If was motonotically decreasing and bounded below, then it would have been convergent by Monotone Convergence Theorem.
Let's consider if it is not below below, i.e.
Find the limit in each of this case.
Hence, it will be unbounded. See the full solution and proof idea below.