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M-D Sequences (Posted on 2014-11-09) Difficulty: 3 of 5


Let the sequence of real numbers { rk } be defined by
   rk = ak                                     if k = 1

      = ak*[ 1 - ( ak/[ 2*rk-1 ] )2 ]           if k > 1.
Prove that { rk } is a
strictly monotonically decreasing sequence with
   ak > rk > 0                                 for k > 1,
if the sequence of real numbers { ak } is a
monotonically decreasing sequence with
   ak > 0                                      for k ≥ 1.

No Solution Yet Submitted by Bractals    
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re(2): What am I missing? Comment 3 of 3 |
(In reply to re: What am I missing? by Bractals)

BTW for your a(k) = 1 case, r(k) = sqrt[ (k+1)/(2k) ].
  Posted by Bractals on 2014-11-09 12:36:24

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