Given {an}, {bn} two monotone sequences of real numbers and that Σ anbn is convergent, which of the following is true?

1
Σ an is convergent and Σ bn is convergent
2
At least one of Σ an, Σ bn is convergent
3
{an} is bounded and {bn} is bounded
4
At least one of {an}, {bn} is bounded
5
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