Using the Monotone Convergence Theorem to Prove a Recursive Sequence Converges: Example 1

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We consider a recursive sequence. We show that the sequence is bounded and monotone. We apply the Monotone Convergence Theorem to show that the sequence converges. This is our first example.

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  1. Mike, the Mathematician
  2. recursive sequences
  3. monotone convergence theorem
  4. mike the mathematician
  5. mike dabkowski math
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Комментарии
Автор

You are the best, thank you. I have been having trouble proving convergence with recursive sequences. Appreciate it!

scienceappreciator
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What would the be process for lets say x_1 = a (a is from the set of the Reals), x_{n+1} = x^2_n + x_n? This I already calculated and the sequence converges to 0 for any a from (-1, 1) but how do I prove it? Or is it neccessary to always prove this stuff via induction?

danilojonic
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why we consider that an is bigger than one half?

KefaleLiche