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

http://lighthousegraphicdesign.com/images/real2.png

Printable View

- Oct 2nd 2008, 12:20 PMuniversalsandboxShow the sequence is decreasing
I have attached a picture of the question. How would you go about showing this? Thanks.

http://lighthousegraphicdesign.com/images/real2.png - Oct 2nd 2008, 02:14 PMCaptainBlack
- Oct 2nd 2008, 02:22 PMuniversalsandbox
- Oct 2nd 2008, 02:38 PMicemanfan
I work out that if $\displaystyle x_n > \frac{a}{x_n}$,

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

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

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

As long as $\displaystyle x_n > \frac{a}{x_n}$, then the function will be decreasing, but I can't find a way to show that statement inductively. - Oct 2nd 2008, 09:24 PMCaptainBlack