Suppose f: R →(0, ∞) be a differentiable function such that 5 f(x+y)=f(x) · f(y), x, y R. If f(3)=320, then Σ n=0 ⁵ f(n) is equal to:

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Morning shift · Q4211

JEE Main 202330 Jan, Morning shiftMathematicsEasyLimit, Continuity and Differentiability420× since 2002

Suppose

f: \mathbb{R} \rightarrow(0, \infty)

be a differentiable function such that

5 f(x+y)=f(x) \cdot f(y), \forall x, y \in \mathbb{R}

. If

f(3)=320

, then

\sum_\limits{n=0}^{5} f(n)

is equal to :