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 Infinite Series

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Consider the infinite series defined by:

     

A) What is the value of r from the ratio test?

 

B) What does this r value tell you about the series?

 

 

I'm online schooled. I don't have anyone to explain this to me properly. I looked up Youtube videos to get a better understanding of the concept and I'm still struggling to see the concept of doing the ratio test. If someone could help, that would be greatly appreciated. I also have to warn you, I ask a lot of questions, so just be prepared. smiley

 Mar 25, 2020

5+0 Answers

 #1
avatar+33615 
+2

I think this has been asked and answered previously somewhere, but I couldn't find where, so:

 

 Mar 25, 2020
 #2
avatar+279 
0

I still feel very confused.. I'm sorry. I got lost at the 1+nth term. Why would you add the 2 on both sides of the fraction? 

After that, I get the work. I tried solving for myself and I got the same answer. So that's the only question I have. 

Thank you for helping, by the way!

 Mar 25, 2020
 #3
avatar+33615 
+2

numerator of nth term   (2n)!

 numerator of n+1th term (2*(n+1))!  =  (2*n + 2*1) ! = (2n + 2)! = (2n+2)*(2n+1)*(2n)!

Alan  Mar 25, 2020
 #4
avatar+33615 
+2

If the numerator is meant to be 2*(n!), the ratio of the n+1th term to the nth term becomes (n+1)/4. This is greater than 1 for all n>3, so the sum still diverges.  However, I think this interpretation of 2n! is unlikely.

 Mar 25, 2020
 #5
avatar+279 
0

That helps a lot. Thank you so much. :)

 Mar 26, 2020

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