# 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| $\displaystyle \leq$ |a|+|b| holds for any two numbers a and b, show that

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

for any n numbers.

Thank you.
• Aug 26th 2011, 08:02 AM
FernandoRevilla
Re: Mathematical induction
Hint: In the induction step consider $\displaystyle a=x_1+\ldots+x_n$ and $\displaystyle b=x_{n+1}$ .
• 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.