Hi!, I have problems with this Proposition

PROPOSITION

Let $\displaystyle d,d^{\prime}$ and $\displaystyle d^{\prime\prime}$ metric space. For any $\displaystyle x,y \in{\mathbb{R^n}}$ we have

$\displaystyle d(x,y)\leq{d^{\prime}(x,y)}\leq{nd^{\prime\prime}( x,y)}$ , where $\displaystyle d(x,y)= [ \displaystyle\sum_{i=1}^N (x_i-y_i)^2]^{1/2}$ ,

$\displaystyle d^{\prime}(x,y)= \displaystyle\sum_{i=1}^N |x_i-y_i|$ , $\displaystyle max_{1\leq{i}\leq{n}} |x_i-y_i|$

I have problems with proof the inequalities