Convergence sequence proof

**Stylis10** · May 16th 2010, 01:37 AM

How would i go about proving this:

Let $(a_n)$ be a sequence convergent to the limit $a \in \mathbb{R}$ . Prove that the sequence of absolute values $(b_n)$ with $(b_n) = |a_n|$ is convergent to the limit $|a|$

**Failure** · May 16th 2010, 03:05 AM

Originally Posted by Stylis10

How would i go about proving this:

Let $(a_n)$ be a sequence convergent to the limit $a \in \mathbb{R}$ . Prove that the sequence of absolute values $(b_n)$ with $(b_n) = |a_n|$ is convergent to the limit $|a|$

Hint: $\big|b_n-|a|\big| = \big||a_n|-|a|\big|\leq |a_n-a|\longrightarrow 0$

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