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Math Help - Mathematical Induction Problem

  1. #1
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    Question Mathematical Induction Problem

    Three parts to this question:
    Consider the sequence { {a_n}}, where a_n = \sqrt{2+\sqrt{2+...+\sqrt{2}}}

    Use Induction to prove that { {a_n}} is an increasing sequence, that is a_{n+1} > a_n for all n = 1, 2, 3...

    Use Induction to prove that { a_n} is bounded from above by 2, that is, a_n < 2 for all n = 1, 2, 3...

    Is { a_n} convergent?
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  2. #2
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    Quote Originally Posted by xxlvh View Post
    Three parts to this question:
    Consider the sequence { {a_n}}, where a_n = \sqrt{2+\sqrt{2+...+\sqrt{2}}}

    Use Induction to prove that { {a_n}} is an increasing sequence, that is a_{n+1} > a_n for all n = 1, 2, 3...

    Use Induction to prove that { a_n} is bounded from above by 2, that is, a_n < 2 for all n = 1, 2, 3...

    Is { a_n} convergent?
    Please write your original sequence properly, in terms of n. At the moment you just have a constant.
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  3. #3
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    ? this is exactly how it appeared on my assignment sheet
    I'm assuming that the number of roots represents "n"
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