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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