Thread: help generalized triangle inequality

X1....Xn are real numbers prove |X1 = X2 + ... + Xn| <= |X1| + |X2| + ..... + |Xn|

Originally Posted by luckyc1423

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).