# Math Help - New Cauchy question

1. ## New Cauchy question

hello ,
im having trouble with proving sqrt(n) is not cauchy.

2. Originally Posted by sandy
hello ,
im having trouble with proving sqrt(n) is not Cauchy.
Cauchy sequences are bounded. Is the sequence $a_n=\sqrt{n}$ bounded?

3. i need to prove it is not cauchy by using the definition

4. Originally Posted by sandy
i need to prove it is not cauchy by using the definition
If $n\ge 6$ then $\sqrt{2n}-\sqrt{n}>1$

5. 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?

6. Alternatively give me any $\epsilon>0$ and N>1, then find an $n>\epsilon$ with n>N (natural numbers are unbounded). Then $n^4>n^2>N$ and moreover

$|\sqrt{n^4}-\sqrt{n^2}|=|n^2-n|=|n(n-1)| \geq n > \epsilon$.

7. thankyo so much for you help

thankyou to all for the help