6. The following statements are false. For each statement please provide a counterexample:

(a) If lim an = 0, then Σan converges.

n→∞

n

(b) Let f be a continuous function and define a sequence an = f(n). If lim an exists and is

equal to a finite real number L, then lim f(x) = L.

n→∞0

2→∞