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
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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 . 2) , b< 0. 3) a< 0, . 4) a< 0 and b< 0. If you can do that, think of as and prove this by induction on n.
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