I need to show that:
$ {\sum\limits_{i=1}^n {|x|} } \leq \sqrt{n\sum\limits_{i=1}^n |x|^2 } $
I tried to square both sides so I would get:
$ \left({\sum\limits_{i=1}^n {|x|} }\right)^2 = \left(\sum_{i=1}^{N}|x_i|^2+2*\sum_{i,j,i j}|x_i||x_j|\right) \leq n\sum\limits_{i=1}^n |x|^2 $
but it just doesn't seem to work...
I know that on both sides we have $n^2$ elements, I just don't know how to compare them.