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

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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
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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
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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