Give an example of a sequence of real numbers with subsequences converging to every real number Im unsure of an example
Give an example of a sequence of real numbers with subsequences converging to every real number

A related question that you can try:
Let $(a_k)_{k\in\mathbb{N}}$ be a real sequence such that $\lim_k a_k=0$, and set $s_n=\sum_{k=1}^na_k$. Then the set of subsequential limits of the sequence $(s_n)_{n\in\mathbb{N}}$ is connected.
