Proving the Limit of x_n = 1/sqrt(n) as n Approaches Infinity

[_Andreas]

Homework Statement

x_n=1/sqrt(n)

Prove that lim x_n = 0 as n approaches infinity

Homework Equations

E > 0

The Attempt at a Solution

There is a natural number N such that N>1/sqrt(E). There is also a number n>N>1/sqrt(E) <==> sqrt(n)>1/sqrt(sqrt(E)) ==> E>sqrt(sqrt(E))>1/sqrt(n). If this last inequality is correct, I can prove the limit in question. But it can't be, because E<sqrt(sqrt(E)) if 0<E<1. So, what should I do instead?

 

[Dick]

You've got this all twisted around. You want 1/sqrt(n)<E for n>N. So you want N>1/E^2.

 

[_Andreas]

You've got this all twisted around. You want 1/sqrt(n)<E for n>N. So you want N>1/E^2.

I see; it's N I'm after. Thank you!