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Math Help - help generalized triangle inequality

  1. #1
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    help generalized triangle inequality

    X1....Xn are real numbers prove |X1 = X2 + ... + Xn| <= |X1| + |X2| + ..... + |Xn|
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  2. #2
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    Quote Originally Posted by luckyc1423 View Post
    X1....Xn are real numbers prove |X1 = X2 + ... + Xn| <= |X1| + |X2| + ..... + |Xn|
    Use the fact,

    |a+b|<=|a|+|b|.

    Say you have 3 (for simplicity sake).

    |x1+x2+x3|=|(x1+x2)+x3|<=|x1+x2|+|x3|<=|x1|+|x2|+| x3|

    Same argument for n>3.

    (You can use induction).
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