Let f(x) be a real differentiable function such that f(0) = 1 and… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 22 January, Shift 1Linear Differential Equations

Let $f(x)$ be a real differentiable function such that $f(0) = 1$ and $f(x + y) = f(x)f'(y) + f'(x)f(y)$ for all $x, y \in \mathbb{R}$ . Then $\sum_{n=1}^{100} \log_e f(n)$ is equal to :

A
$2384$
B
$2525$
C
$5220$
D
$2406$

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