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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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Comments: ( Back to comment list | You must be logged in to post comments.)
re: What am I missing? | Comment 2 of 3 |
(In reply to What am I missing? by Steve Herman)

No. My problem.


When I looked at the problem as submitted the first time
the square root symbol looked like a little v.

So I edited it by removing the little v and not replacing it
with sqrt. 

The value for r(k) with k greater than one should be

r(k) = 
ak*sqrt[ 1 - ( ak/[ 2*rk-1 ] )2 ].

  Posted by Bractals on 2014-11-09 12:12:16
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