Show the sequence is decreasing

**universalsandbox** · October 2nd 2008, 12:20 PM

I have attached a picture of the question. How would you go about showing this? Thanks.

**CaptainBlack** · October 2nd 2008, 02:14 PM

Originally Posted by universalsandbox

I have attached a picture of the question. How would you go about showing this? Thanks.

Is/are there an extra condition/s that is/are missing here?

RonL

**universalsandbox** · October 2nd 2008, 02:22 PM

Originally Posted by CaptainBlack

Is/are there an extra condition/s that is/are missing here?

RonL

Ex:

let a=2, xknot = 1

then

x(sub1) = (1/2)(xknot + 2/xknot) = 3/2

x(sub2) = (1/2)( x(sub1) + 2/(xsub1) ) = 17/2 etc.

**icemanfan** · October 2nd 2008, 02:38 PM

I work out that if $x_n > \frac{a}{x_n}$ ,

$x_n + \frac{a}{x_n} > \frac{2a}{x_n}$

$0.5\left(x_n + \frac{a}{x_n}\right) > \frac{a}{x_n}$

$x_{n+1} > \frac{a}{x_n}$ .

As long as $x_n > \frac{a}{x_n}$ , then the function will be decreasing, but I can't find a way to show that statement inductively.

**CaptainBlack** · October 2nd 2008, 09:24 PM

Originally Posted by universalsandbox

Ex:

let a=2, xknot = 1

then

x(sub1) = (1/2)(xknot + 2/xknot) = 3/2

x(sub2) = (1/2)( x(sub1) + 2/(xsub1) ) = 17/2 etc.

Compare what happens when $x_0>\sqrt{a}$ with what happens when $x_0<\sqrt{a}$ with what happens when $x_0=\sqrt{a}.$

RonL

Thread: Show the sequence is decreasing

LinkBack

Thread Tools

Display

Show the sequence is decreasing

Similar Math Help Forum Discussions

does the sequence necessarily become decreasing??

prove sequence is decreasing using PMI

How do I show that 1/n^(1/4) is decreasing?

show series is decreasing

Show a sequence is decreasing

Search Tags