# Math Help - Mathematical induction

1. ## 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.

2. ## Re: Mathematical induction

Hint: In the induction step consider $a=x_1+\ldots+x_n$ and $b=x_{n+1}$ .

3. ## Re: Mathematical induction

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

4. ## Re: Mathematical induction

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.