Science:Math Exam Resources/Courses/MATH101/April 2011/Question 01 (f)
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Question 01 (f) 

For this question, the exam asks to put your answer in the box provided but also to show your work. This question is worth 3 marks. Full marks is given for correct answers placed in the box and at most 1 mark is given for an incorrect answer. You are required to simplify your answers as much as possible. Determine whether the series is convergent or divergent. In case it is convergent, compute its sum. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Note 
Hint 2 

Use the formula for the sum of a geometric series. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The series can be rewritten as
This is a geometric series with common ratio , so it converges. Recall that a convergent geometric series has sum
Note that to use this formula we need to adjust the series to start at We get
