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Prove that lim gn for n→∞ exists, and find it.

  1. Sep 9, 2009 #1
    Suppose g1 , g2 ,... are any numbers that satisfy the inequalities
    0 < gn < 1 and (1 − gn )gn+1 > 1/4 for all n.

    Prove that lim gn for n→∞ exists, and find it.


    I need well substantiated answer! Thanks.
     
  2. jcsd
  3. Sep 9, 2009 #2

    LCKurtz

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    Is this a homework problem? I'll give you a hint. Show:

    [tex]\frac 1 {4(1-x)} \ge x[/tex]

    on the interval, consequently showing your sequence gn is increasing. Then...
     
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