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

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

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

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