Consider the sequence where $a_10$, $ka_na_{n+1}$ and $0

Question

I could get that
$a_1>k^n a_1 > a_{n+1}$ and therefore $0geqlim a_n$
But I can't find a lower bound for the squeeze theorem or something about monotonicity.
Any idea about this?

DanielWainfleet · Answer

Not without additional conditions (e.g. if $forall n,(a_nge 0),$).
For example if $k=1/2$ and $a_1=1$ and $a_n=-n$ for $n>1.$

Consider the sequence where $a_1>0$, $ka_n>a_{n+1}$ and $0<k<1$. Can we say it converges?

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