Consider a function f: ℕ → ℝ satisfying f(1) + 2f(2) + 3f(3) + …… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 29 January, Shift 2Sum of Series

Consider a function $f : \mathbb{N} \to \mathbb{R}$ satisfying $f(1) + 2f(2) + 3f(3) + \dots + x f(x) = x(x + 1) f(x)$ for $x \geq 2$ , with $f(1) = 1$ . Then $\dfrac{1}{f(2022)} + \dfrac{1}{f(2028)}$ is equal to:

A
$8200$
B
$8000$
C
$8400$
D
$8100$

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