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| Math Central | Quandaries & Queries |
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Question from James, a teacher: I need to prove a problem by induction regarding the Triangle Inequality. The problem is abs(a1 + a2 +...+an) <= abs(a1) + abs(a2) +...+ abs(an). |
James,
For problems like this, the key idea is to write
abs(a1 + a2 + ... + an) = abs(a1 + a2 + ... + (an-1 + an)).
The expression on the right hand side is a sum of n-1 terms. That lets you use the induction hypothesis to get
<= abs(a1) + abs(a2) +...+ abs(an-1+an)
and then apply the base case to the last term.
Good luck.
Victoria
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