# Math Help - absolute value proof

1. ## absolute value proof

let x1, x2, ..., xn-1,xn be in R and n be in N prov that |x1+x2+...+xn-1+xn| is less than or equal to |x1|+|x2|+...+|xn-1|+|xn|

hint use induction and triangle inequality

2. Can you prove the simplest case? If a and b are real numbers, what can you say about |a+ b| and |a|+ |b|. Try cases:
1) a and b both $\ge 0$.
2) $a\ge 0$, b< 0.
3) a< 0, $b\ge 0$.
4) a< 0 and b< 0.

If you can do that, think of $x_1+ x_2+ \cdot\cdot\cdot+ x_{n-1}+ x_n$ as $(x_1+ x_2+ \cdot\cdot\cdot+ x_{n-1})+ x_n$
and prove this by induction on n.