Science:Math Exam Resources/Courses/MATH105/April 2014/Question 01 (l)
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Question 01 (l) 

Evaluate . 
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 

Remember that if . 
Hint 2 

Remember that you can reindex series. If you want a series to start from instead of , you can do this by replacing the in the series terms by . 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. We have With the first equality, we rewrote the geometries series starting from in order to apply for . This was accomplished by reindexing. In the second equality, we split the sum into two and factored out from the first sum. 