Decide whether the following propositions are true or false: (1) If lim an = e bn = + 3 an then lim = bn (2) If an 0 and bn 8 then 0 (3) If an and ...

Decide whether the following propositions are true or false: (1) If lim an = e bn = + 3 an then lim = bn (2) If an 0 and bn 8 then 0 (3) If an and bn are both non-convergent sequences, then a an + bn does not converge. (4) If lim an and lim n = n 00 an then lim = - 1. n->00 bn (5) If an converges then also converges.

(1) If lim an = e bn = + 3 an then lim = bn
(2) If an 0 and bn 8 then 0
(3) If an and bn are both non-convergent sequences, then a an + bn does not converge.
(4) If lim an and lim n = n 00 an then lim = - 1. n->00 bn
(5) If an converges then also converges.
All propositions are false.
All propositions are true.
Propositions (2) and (3) are true and propositions (1), (4) and (5) are false.
Propositions (1), (4) and (5) are true and propositions (2) and (3) are false.
Propositions (1), (2) and (3) are true and propositions (4) and (5) are false.