Summation of Function Values (Jee Mains)

Evaluation of Limits

Medium

Summation of Function Values

Let f : ${\Bbb R}$ → ${\Bbb R}$ be a continuous function satisfying f(0) = 1 and f(2x) – f(x) = x for all x ∈ ${\Bbb R}$ . If $\mathop {\lim }\limits_{n \to \infty } \left\{ {f\left( x \right) - f\left( {\frac{x}{{{2^n}}}} \right)} \right\} = G\left( x \right)$ , then $\sum\limits_{r = 1}^{10} {G\left( {{r^2}} \right)}$ is equal to

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