Finding a sequence $a_n$ that diverges such that $\|a_n\|$ converges (in $\mathbb{R}$)
I am having a hard time finding an example that works. An example or hint would be greatly appreciated.
2026-03-25 07:42:59.1774424579
Finding a sequence $a_n$ that diverges such that $\|a_n\|$ converges (in $\mathbb{R}$)
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Consider $a_n = (-1)^n$. It does not converge but $\|a_n\| = 1, \forall n\in\mathbb{N}$.