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?
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?