Reverse triangle inequality for n real numbers

[realanony87]

I have been trying the proof of the reverse triangle inequality for n+1 real numbers:

|x-y1-y2-y3-...-yn| \geq | |x| - |y1| - |y2| - |y3| - ...-|yn| |

I know the proof of the reverse triangle inequality for 2 real numbers and the triangle inequality for n numbers. can somebody help ?

 

[tim_lou]

this inequality isn't even true, take x=0 for instance, and y1=1, y2=-1, y3=1...
when n is even, you get zero on left hand side and n on the right hand side.

 

[realanony87]

There goes 1 hour trying to prove something which is easily disproved. It was one exercise in a Real analysis book. Well atleast I learned how to be critical of everything now ^^