This is my suggestion, I hope it will help you
Then the f_n(x) converges pointwise if lim (f_n(x))--> f(x) as n--> infinity
Thus, in this case lim (f_n(x)) = 0 as n-->infinity
Hence, f_n ---> f pointwise where f(x) = 0
That is the way I find convergence pointwise of a function, and if you are given the interval of the function, for example I = [0,1]. Then if x inside that interval then f_n ---> f pointwise.