Do you see yourself NOW on the terminal/computer/recording screen as one of the 7 examples below? If you do, please keep the setting (you and the computer) the way it is, throughout the exam.  If you don’t, adjust now before proceed. You will be deducted 20% of the points from each problem that you are not following the direction and face consequences as stated in the syllabus and the announcement on “Academic Integrity”.

Any mistake in the following process? If so, where is it initiated?  Evaluate  

Find the Taylor series for  centered at 1 if State the radius of convergence.

You are given the alternating series .  You determine the following: 1. , and it diverges by a Comparison Test. 2. diverges by the Alternating Series Test. What can you then conclude?

Determine whether the statement is true or false.   If

The fifth degree term in the binomial series for  is

Determine if the following argument and conclusion is true or false.   Apply the Alternating series Test on . 1. We verify (clearly, this is true). 2. We observed that (clearly, this is true too) Therefore, the series converges absolutely.  

Evidence is “material” if it is logically connected with some fact that is at issue.

Any mistake in the following process? If so, where did it initiated?  Evaluate  

Determine if converges. If it converges, find its sum. State the common ratio [answer1] This series [answer2]. The sum of the series [answer3]