Convergence in the product and box topology

[calvin22]

Hi. Can I have some help in answering the following questions? Thank you.

Let {f_n} be a sequence of functions from N(set of natural numbers) to R(real nos.) where
f_n (s)=1/n if 1<=s<=n
f_n (s)=0 if s>n.
Define f:N to R by f(s)=0 for every s>=1.
a) Does {f_n} (n=1 to inf) converge to f in the R^N (cartesian product) endowed with the product topology?
b) when endowed with the box topology?

Thanks again.

 

[Landau]

Of course you can can get help, but first tell us what you have tried. The least you can do is trying to come up with some relevant facts about the box and product topologies (such as their definitions, what it means for a sequence to converge in them, and the like).