All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

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

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 No Rating

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

 Search: Search body:
Forums (0)