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(x/2ⁿ)] = G(x), then Σ r=1 ¹⁰ G(r²) is equal to:

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q135

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let f: \mathbb{R} \to \mathbb{R} be a continuous function satisfying f(0) = 1 and f(2x) - f(x) = x for all x \in \mathbb{R}. If \lim_{n\to\infty} [f(x) - f(x/2^n)] = G(x), then \sum_{r=1}¹⁰ G(r²) is equal to:

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

More on Limit, Continuity and Differentiability

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

More on Limit, Continuity and Differentiability