perplexus.info :: Just Math : M-D Sequences

M-D Sequences (Posted on 2014-11-09)

Let the sequence of real numbers { r_k } be defined by
r_k = a_k if k = 1 = a_k*[ 1 - ( a_k/[ 2*r_k-1 ] )² ] if k > 1.
Prove that { r_k } is a
strictly monotonically decreasing sequence with
a_k > r_k > 0 for k > 1,
if the sequence of real numbers { a_k } is a
monotonically decreasing sequence with
a_k > 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) = a_k*sqrt[ 1 - ( a_k/[ 2*r_k-1 ] )² ].

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

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