(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]\sum_{k=1}^{\infty} a_k[/tex] converges and [tex]a_k/b_k \to 0[/tex] as [tex]k\to \infty[/tex], then [tex]\sum_{k=1}^{\infty} b_k[/tex] converges.

2. Relevant equations

It is true or false.

3. The attempt at a solution

I think it is false and here is my counterexample. Let [tex]a_k = 0,b_k=\frac{1}{k}[/tex]. This satisfies our initial conditions of [tex]\sum_{k=1}^{\infty} a_k[/tex] converges and [tex]a_k/b_k \to 0[/tex] as [tex]k\to \infty[/tex] but [tex]\sum_{k=1}^{\infty} b_k[/tex] diverges.

Is this correct?

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# Homework Help: Converges Proof

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