- #1
CyberShot
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Homework Statement
Show that
|x_1 + x_2 + · · · + x_n | ≤ |x_1 | + |x_2 | + · · · + |x_n |
for any numbers x_1 , x_2 , . . . , x_n
Homework Equations
|x_1 + x_2| ≤ |x_1| + |x_2| (Triangle inequality)
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| ?