If we want to use the Comparison Test to show that a series sigma^infinity_k = 1

Question

If we want to use the Comparison Test to show that a series sigma^infinity_k = 1 a_k with non-negative terms diverges, we need a series sigma^infinity_k = 1 b_k with non-negative terms such that sigma^infinity_k = 1 b_k _____ and a_k ____ b_k for all but finitely many k. Please explain, I have a big test tomorrow morning. Do not copy and paste from wolfram. Please hand write and write quite legibly for everyone to read. Write very legibly and neatly so that it is easy to read out and understand. Do not let the edges of a scanned or pictured image are cropped, resulting illegible scripts. Do not skip steps. Never use the multiply symbol (times) between numbers and letters. I need solutions and answers as soon as possible. Many thanks.

Explanation / Answer

There are two important aspects of comparison test:

1) If a smaller series is divergent, then the bigger series must diverge too

2) If a bigger series is convergent, then the smaller series must converge too

In the given question we will use the first aspect of comparison.

We need prove that series an is divergent, therefore, we need to compare it to a smaller series bn which is divergent. Therefore, you can fill the blanks as "divergent" and ">="

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