3. True or False.

(a) If limn→∞ (an + bn) diverges, then both {an} and {bn} diverges.

(b) If {an} converges and {bn} is bounded, then {anbn} converges.

(c) If an and Σbn both diverge, then (an+bn) also diverges.

(d) Let f be a positive, continuous function of a for x ≥ 1, and f f(x) dx converges.

1 an Σ1 f(n) converges.

Then

=

=1