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Math Help - Convergence sequence proof

  1. #1
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    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|
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by Stylis10 View Post
    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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