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Math Help - [SOLVED] prove inf {|s_n|} = 0

  1. #1
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    [SOLVED] prove inf {|s_n|} = 0

    Basically, I need to show that

    \lim_{n\to\infty}s_n=0, where

    s_n=nk^n(1-k^2) with |k|>1.

    I have already shown that |s_n| is decreasing for all n\geq N, where

    N>\frac{|k|}{1-|k|}

    Thus I need only show that \inf\{|s_n|\}=0. The problem is, I'm at a loss to do so.

    Any ideas?
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  2. #2
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    Quote Originally Posted by hatsoff View Post
    Basically, I need to show that

    \lim_{n\to\infty}s_n=0, where

    s_n=nk^n(1-k^2) with |k|>1.

    I have already shown that |s_n| is decreasing for all n\geq N, where

    N>\frac{|k|}{1-|k|}

    Thus I need only show that \inf\{|s_n|\}=0. The problem is, I'm at a loss to do so.

    Any ideas?
    Are you sure for |k|>1 |s_{n}| is decreasing ??
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  3. #3
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    Quote Originally Posted by xalk View Post
    Are you sure for |k|>1 |s_{n}| is decreasing ??
    Hey, you're right! I forgot to flip the inequality when I multiplied by (1-|k|).

    Thanks!
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