Science:Math Exam Resources/Courses/MATH220/April 2011/Question 07 (a)
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Question 07 (a) 

Let be a sequence of real numbers defined by Prove that 
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? 
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Hint 

Use induction! 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We will prove this by induction. The first case, is easy to go through, indeed so the first term of the sequence matches the general formula. You can do as many initial cases as you want, but remember, you have to at least one to get your argument started. Then comes the general case. We say: assume that the statement is true for all values of up to . We will show that the statement is also true for . By definition of the sequence , we know that And we also assume that the statement is true up to hence Combining these two facts together, we obtain that which is the claimed statement to be proved and so concludes our proof. 