Show sequance is monotonic Let $x>0$ (fixed) and $n$ be natural. Show that $$\displaystyle (x^n+x^{n-1}+...+1)^{\frac{1}{n}}$$ is monotonic. 
I tried by induction but didn't work but intuition tells me it's decreasing. 

The first couple are decreasing at least:
$(x+1)^2-(x^2+x+1)^1=x$
$(x^2+x+1)^3-(x^3+x^2+x+1)^2=x^5+3x^4+3x^3+3x^2+x\\=x(x+1)(x^3+x^2+x+1)+x^2(x^2+x+1)$
Next is $(x^3+x^2+x+1)^4-(x^4+x^3+x^2+x+1)^3$, which is
$$x^{11}+4x^{10}+10x^9+16x^8+22x^7+25x^6+22x^5+16x^4+10x^3+4x^2+x$$
