I want to prove this inequality but it does not work with me, need help $$\frac{c_{n}R}{(|x|+R)^{n}}+\sum_{k=0}^{\infty}\frac{1}{(1+2^{k})^n}\frac{c_{n}(2^{k+1}R)^{n}}{(|x|+2^{k+1}R)^{n}}\leq \frac{C_{n}\log(e+\frac{|x|}{R})}{(1+\frac{|x|}{R})^{n}}$$ the indication said , we can get this estimate by summing separatly over k satisfying $2^{k+1}\geq \frac{|x|}{R}$ and $2^{k+1}\leq \frac{|x|}{R}$
$c_n,C_n$ are constants which depend only on the dimension of $\mathbb{R}^n$ and $R>0$ and $x \in \mathbb{R}^n$