$$\eqalign{ & \mathop {\lim }\limits_{n \to \infty } {a_n} = 3 \cr & {b_n} = |{a_n} - 1| \cr} $$
Hence,
$$\mathop {\lim }\limits_{n \to \infty } {b_n} = |3 - 1| = 2$$
Is it right to say that?
If so, is it sufficent for a proof?
2026-04-04 20:59:36.1775336376
limit of an absolute sequence: ${b_n} = |{a_n} - 1|$
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If you're asking, then it isn't sufficient. Consider this $$\lim \limits _{n\to \infty}a_n=3\implies \lim \limits _{n\to \infty}(a_n)-1=2\implies \left|\lim \limits _{n\to \infty}(a_n-1)\right|=2\mathop{\implies}^{\text{Why?}} \lim \limits _{n\to \infty}\left|(a_n-1)\right|=2.$$