+3 votes
74 views

Let $\left\{a_{n}\right\}$ be a sequence of real numbers such that $|a_{n+1}-a_{n}|\leq \frac{n^{2}}{2^{n}}$ for all $n \in \mathbb{N}$. Then

1. The sequence $\left\{a_{n}\right\}$ may be unbounded.
2. The sequence $\left\{a_{n}\right\}$ is bounded but may not converge.
3. The sequence $\left\{a_{n}\right\}$ has exactly two limit points.
4. The sequence $\left\{a_{n}\right\}$ is convergent.
| 74 views

+3 votes
0 answers
1
+2 votes
0 answers
2
+2 votes
0 answers
3
+1 vote
0 answers
4
+2 votes
1 answer
5
+1 vote
0 answers
7