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
true, or false.
if someone could perhaps give an explanation, that would be awesome, thanks
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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.
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.