How can mathematical induction be used to prove the triangle inequality?

[pzzldstudent]

My professor said this was the triangle inequality. We're to use mathematical induction to prove it. I've gotten some work done, and after "proving" it, it just seems to easy. :|

http://answerboard.cramster.com/advanced-math-topic-5-321495-0.aspx" .

 

[statdad]

The work you've done is essentially correct - the idea is to write

$$|a_1 + a_2 + \dots + a_k + a_{k+1}| = |(a_1 + a_2 + \dots + a_k) + a_{k+1}|$$

then use the hint once, then your induction hypothesis.

 

[pzzldstudent]

thank you

thanks!