Question: What does the graph of gn(x) look like as n increases?
Here is the graph of f(n).
Question: Sketch the graphs of f(x) gn(x) and compare it with the graphs of gn(x) and f(x). Judging by the graph, what do you think converges to?
Question: Now, what we really want is to have a sequence of functions converging to f. Can we use this last observation to make some functions that converge to f(t)?