(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that

|x_1 + x_2 + · · · + x_n | ≤ |x_1 | + |x_2 | + · · · + |x_n |

for any numbers x_1 , x_2 , . . . , x_n

2. Relevant equations

|x_1 + x_2| ≤ |x_1| + |x_2| (Triangle inequality)

3. The attempt at a solution

I tried using the principle of induction here, but to no avail.

Can I induct on the basis |x_1| ≤ |x_1| ?

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# Homework Help: Generalized triangle inequality

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