(adsbygoogle = window.adsbygoogle || []).push({}); Are my answers right? (Calculus! YAY!!!)

I need to know if my answers to these questions are correct... Any help is very much appreciated and thanks in advance. :)

Questions = bold

Does [tex]\sum \frac {ln k}{\sqrt k}[/tex] converge or diverge? limits are 0 to infinity.

answer: diverge because the limit of [tex]a_n[/tex] goes to 1 and not zero.

Does [tex]\sum \frac {cos^2 k}{k^2 +1}[/tex] converge or diverge? Limits are 0 to infinity.

answer: converge because it's smaller then [tex]\sum \frac {1}{k^2}[/tex] which converges because of the p-series test... I'm not sure about this since k is inside cosine... :(

What are the radius and domain of this power series: [tex]\sum \frac {n(x-3)^n}{2^(n+1)}[/tex] limits are 0 to infinity.

answer: Radius is2and domain is[ 1, 5)...

What I did here was the ratio test which ended up with a limit of [tex]\frac {1}{2}[/tex] and then got to x being between 1 and 5. I checked both points and the series diverges with 5 plugged in for x and converges (alternate series) when 1 is plugged in...

whew. Again, thanks for any help. This is pretty important right now.

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# Homework Help: Are my answers right? (Calculus! YAY )

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