Chapter 2.2, Problem 48E

Assume the statement from Exercise 30 in section 2.1 that $|x+y|\le \left|x\right|+\left|y\right|$ for all $x$ and $y$ in $Z$. Use this assumption and mathematical induction to prove that

$|a_1+a_2+\mathrm{...}+a_n|=\left|a_1\right|+\left|a_2\right|+\mathrm{...}+\left|a_n\right|$

for all positive integers $n\ge 2$ and arbitrary integers $a_1,a_2,\mathrm{...},a_n$.