The “secret” was to unlocking the question

Question 4 in midterm is based on convergence of series. When we start doing this question, we should think of the tests about series we learned.(Ratio, Comparison, Limit Comparison, Alternating and Diverge Test.) This question is about the content of Ratio Test. The thing we should notice is that the value of the ratio should be less that absolute 1 if we want to prove the series converges, and the value of the ratio should be bigger or equal to absolute 1 if we want to prove the series diverges. And then, we can solve this question based on the value of the ratio.

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