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Math Help - Induction

  1. #1
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    Induction

    Suppose that 0 < x_1 < 2 and x_(n+1) = sqrt(2 + x_n).
    Prove that 0 < x_n < x_(n+1) < 2 for all n Natural Numbers.
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  2. #2
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    Suppose that K > 1\,\& \,x_{K - 1}  < x_K  < 2 is true.
    \begin{array}{rclcl}<br />
   {x_{K - 1}  + 2} &  <  & {x_K  + 2} &  <  & 4  \\<br />
   {\sqrt {x_{K - 1}  + 2} } &  <  & {\sqrt {x_K  + 2} } &  <  & {\sqrt 4 }  \\<br />
   {x_K } &  <  & {x_{K + 1} } &  <  & 2  \\ \end{array}
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