Science:Math Exam Resources/Courses/MATH101/April 2018/Question 08 (ii)
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Question 08 (ii) |
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Calculate |
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! |
Hint |
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Part of the series will telescope. |
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. We start by splitting the series Now the second series will telescope. Observe that for any positive integer , we have so we have It remains to calculate the series
Now the series is a geometric series, so using the formula for the geometric series we get that
It follows that Answer: The correct answer is . |