New Cauchy question

• Apr 23rd 2010, 01:05 PM
sandy
New Cauchy question
hello ,
im having trouble with proving sqrt(n) is not cauchy.
• Apr 23rd 2010, 01:25 PM
Plato
Quote:

Originally Posted by sandy
hello ,
im having trouble with proving sqrt(n) is not Cauchy.

Cauchy sequences are bounded. Is the sequence $\displaystyle a_n=\sqrt{n}$ bounded?
• Apr 23rd 2010, 01:51 PM
sandy
i need to prove it is not cauchy by using the definition
• Apr 23rd 2010, 01:58 PM
Plato
Quote:

Originally Posted by sandy
i need to prove it is not cauchy by using the definition

If $\displaystyle n\ge 6$ then $\displaystyle \sqrt{2n}-\sqrt{n}>1$
• Apr 23rd 2010, 02:33 PM
Drexel28
Quote:

Originally Posted by sandy
hello please i need help proving sqrt(n) is not a cauchy sequence

Hi. How about that it doesn't converge?
• Apr 23rd 2010, 05:13 PM
Focus
Alternatively give me any $\displaystyle \epsilon>0$ and N>1, then find an $\displaystyle n>\epsilon$ with n>N (natural numbers are unbounded). Then $\displaystyle n^4>n^2>N$ and moreover

$\displaystyle |\sqrt{n^4}-\sqrt{n^2}|=|n^2-n|=|n(n-1)| \geq n > \epsilon$.
• Apr 24th 2010, 01:00 PM
sandy
thankyo so much for you help

thankyou to all for the help