+0  
 
0
69
2
avatar+277 

Consider the series 1/4 + 3/2 + 11/4 + 4 + 21/4 + ....

Does the series converge or diverge?

 

The series [converges, diverges].

You conclude this because the series is [arithmetic, geometric, or neither].

 


I concluded that the series is arithmetic because the difference is 5/4. I can't figure out if it converges or diverges though. If someone could help me, I'd appreciate it!

 Jun 8, 2020
 #1
avatar
+1

Since you determined the common difference of 5/4 and since there are no "-" signs in the sequence, it could only mean one thing. That each subsequent term is bigger than the previous term by 5/4, hence you must come to the conclusion that it will eventually diverge, or become bigger and bigger as terms tend to infinity.

 Jun 8, 2020
 #2
avatar+277 
0

Ahh, so it converges it must be less than one or a negative. And if it diverges, it must be greater than one. That makes a lot more sense! Thank you so much! 

auxiarc  Jun 8, 2020

18 Online Users

avatar
avatar