## Calculus: Early Transcendentals 8th Edition

Consider $a_{n}=(-1)^n$ and $b_{n}=(-1)^{n+1}$ (Both diverge) Then $a_{n}b_{n}=(-1)^n\times (-1)^{n+1}= (-1)^{2n+1}=-1$ Since only one of them is always negative for any $n$, it converges. Hence, the statement is false.