1. ## 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?

2. ## Re: limit 1/sqrt(n)

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 $\epsilon>0$.

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

Can you finish?

3. ## 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→∞

Is that not the definition I need to prove this limit?

4. ## Re: limit 1/sqrt(n)

Carla1985
there nothing wrong with your proof but follow Plato's method it is more rigorous...besides your sequence is a null sequence therefore a=0.

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# lim1/root-n convergea

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