hello ,

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

Please help.

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- Apr 23rd 2010, 01:05 PMsandyNew Cauchy question
hello ,

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

Please help. - Apr 23rd 2010, 01:25 PMPlato
- Apr 23rd 2010, 01:51 PMsandy
i need to prove it is not cauchy by using the definition

- Apr 23rd 2010, 01:58 PMPlato
- Apr 23rd 2010, 02:33 PMDrexel28
- Apr 23rd 2010, 05:13 PMFocus
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 PMsandy
thankyo so much for you help

thankyou to all for the help