ok guys i'm trying to get my head around pointwise convergence.

I'm working through an example, I = [0,1]

fn(x) = 0 ,for x=0

= ((-1)^n)n ,for x E (0,1/n]

= 0 ,for x E (1/n,1]

The answer:

pick some N large enough so that it satisfies 1/N < x. Then fn(x) = 0 for all n less than or equal to N and so fn(x) ---> 0

I can't seem to see why how picking an N proves the convergence?

any help would be much appreciated