# limit 1/sqrt(n)

• Feb 14th 2013, 06:32 AM
carla1985
limit 1/sqrt(n)
We've been doing proving limits and sequences in class and have been given this as one of the practice questions.

prove lim 1/sqrt(n)=0

I've done |1/sqrt(n)-0|=1/sqrt(n)<E so N(E)=[1/E^2]+1 but that seems waaay to simple to the ones we did before, is there another way of doing this or that literally all I need to do?
• Feb 14th 2013, 07:02 AM
Plato
Re: limit 1/sqrt(n)
Quote:

Originally Posted by carla1985
We've been doing proving limits and sequences in class and have been given this as one of the practice questions.

prove lim 1/sqrt(n)=0

These proofs must begin with: Suppose that $\displaystyle \epsilon>0$.

Then we know that $\displaystyle \epsilon^2>0$ so $\displaystyle \left( {\exists N \in \mathbb{N}} \right)\left[ {n \geqslant N \Rightarrow \frac{1}{n} < \epsilon ^2 } \right]$.

Can you finish?
• Feb 14th 2013, 07:48 AM
carla1985
Re: limit 1/sqrt(n)
I'm a little confused by what definition that is. In class we had the definition of convergence to be:

Let
(an)n∈N be a sequence of real numbers. The sequence is called convergent to a ∈ R if for every ε > 0 there exists N =N(ε)∈N such that

|an−a|<ε for all n≥N(ε).
If (an)n∈N converges to a we call a the limit of (an)n∈N and we writelim an = a.
n→∞