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Apr
6
comment True or false statement about a simple limit of product
What if for all but a finite number of terms $b_n\geq c, c>0$? Can we say then that $\lim_{n\to\infty}(a_n)=0$? (see my reasoning in the comments above)
Apr
6
comment True or false statement about a simple limit of product
@Winther - I think it is true because $$\lim_{n\to\infty}(a_nb_n)=0\Rightarrow\forall\varepsilon>0,\exists N,\forall n>N:|a_nb_n|<\varepsilon\Rightarrow|a_n|<\frac{\varepsilon}{b_n}\Rightarrow|a_n|‌​<\frac{\varepsilon}{c}\Rightarrow\\\Rightarrow\lim_{n\to\infty}a_n=0$$ Am I correct?
Apr
6
comment True or false statement about a simple limit of product
@Winther - what if $c>0$, and for all but a finite number of terms $b_n\geq c$. Can we say then that $\lim_{n\to\infty}(a_n)=0$?
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