Let f: R → R be a continuous function satisfying f(0)=1 and f(2 x)-f(x)=x for all x ∈ R. If lim_n → ∞{f(x)-f(x/2^n)}=G(x), then Σ_r=1^10 G(r^2) is…

Let $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function satisfying $\displaystyle f(0)=1$ and $\displaystyle f(2 x)-f(x)=x$ for all $\displaystyle x \in \mathbb{R}$. If $\displaystyle \lim _{n \rightarrow \infty}\left\{f(x)-f\left(\frac{x}{2^n}\right)\right\}=G(x)$, then $\displaystyle \sum_{r=1}^{10} G\left(r^2\right)$ is equal to