# Mathematical induction

• Aug 26th 2011, 07:56 AM
BERMES39
Mathematical induction
Can someone show me how to do the following proof using mathematical induction:

Assuming that the triangle inequality |a+b| $\leq$ |a|+|b| holds for any two numbers a and b, show that

| $x_{1}+x_{2}+...+x_{n}$| $\leq$ | $x_{1}$|+| $x_{2}$|+...+| $x_{n}$|

for any n numbers.

Thank you.
• Aug 26th 2011, 08:02 AM
FernandoRevilla
Re: Mathematical induction
Hint: In the induction step consider $a=x_1+\ldots+x_n$ and $b=x_{n+1}$ .
• Aug 26th 2011, 05:20 PM
BERMES39
Re: Mathematical induction
Thank you for the hint. Still, I will appreciate if someone gives me the full solution.
• Aug 26th 2011, 05:28 PM
TKHunny
Re: Mathematical induction
Quote:

Originally Posted by BERMES39
Thank you for the hint. Still, I will appreciate if someone gives me the full solution.

Wouldn't we all. Come on. Throw us a bone and prove that you can give it a go. Show us ANYTHING.