Divergent sequences....please help...
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Divergent sequences....please help...

[From: ] [author: ] [Date: 12-10-07] [Hit: ]
diverge), but as their product is constant it converges.......
if {an} and {bn} are divergent sequences then {an * bn} is also divergent.

true, or false.

if someone could perhaps give an explanation, that would be awesome, thanks

-
It's false.
a_n = (-1)ⁿ
b_n = (-1)ⁿ⁺¹

Then
(a_n)(b_n) = (-1)²ⁿ⁺¹ = -1

Neither a_n nor b_n converge (i.e. diverge), but as their product is constant it converges.
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