Science:Math Exam Resources/Courses/MATH220/April 2005/Question 05
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Question 05 

Let be real numbers. Prove, using induction, that for all , You may assume the Triangle Inequality in the form for all real numbers x and y. 
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Hint 

Use that 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We use induction. In the base case when we have so the statement is true. Induction step: we assume that holds for some (fixed) value . Then it also holds for : Where the first inequality is true by the triangle inequality and the second by induction hypothesis. This finishes the induction step and so the result is true for all by induction. 