Thread: 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?

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 .

Then we know that so .

Can you finish?

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→∞




so we start with a_n-a and solve for N(ε)
Is that not the definition I need to prove this limit?

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.