Exercise 2.5.5

Question

Assume $\left(a_{n}\right)$ is a bounded sequence with the property that every convergent subsequence of $\left(a_{n}\right)$ converges to the same limit $a \in \mathbf{R}$. Show that $\left(a_{n}\right)$ must converge to $a$.

Ulisse Mini · Accepted Answer

$(a_2, a_3, \dots)$ Is a convergent subsequence, so obviously if $(a_2, a_3, \dots) 	o a$ then $(a_n) 	o a$ also.

Exercise 2.5.5

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Exercise 2.5.5

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