MATH220 April 2005
• Q1 • Q2 • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 •
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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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.
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