# Convergence sequence proof

• May 16th 2010, 02:37 AM
Stylis10
Convergence sequence proof
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 $|a|$
• May 16th 2010, 04:05 AM
Failure
Quote:

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