Let f: \mathbb{R} \rightarrow \mathbb{R} be a continuous function satisfying f(0)=1 and f(2 x)-f(x)=x for all x \in \mathbb{R}. If \lim_{n \rightarrow \infty} \{f(x)-f (\frac{x}{2^n}) \} =G(x), then \sum_{r=1}^{10} G (r^2) is equal to [4 Apr 2025 Shift 1]

Limits, Continuity and Differentiability Part 3

Section: Mathematics

Question : 19 of 69

Marks: +1, -0

Let f:ℝ⟶ℝ be a continuous function satisfying f(0)=1 and f(2x)−f(x)=x for all x∈ℝ.
If

lim

n⟶∞

{f(x)−f(‌

)}=G(x), then

∑

r=1

G(r2) is equal to

[4 Apr 2025 Shift 1]

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