Consider a function \(f:\mathrm{ℕ}\to \mathrm{ℝ}\), satisfying \(f(1)+2f(2)+3f(3)+\ldots +xf(x)=x(x+1)f(x);\) \(x\geq 2\…

Consider a function \(f:\mathrm{ℕ}\to \mathrm{ℝ}\), satisfying \(f(1)+2f(2)+3f(3)+\ldots +xf(x)=x(x+1)f(x);\) \(x\geq 2\) with \(f(1)=1\). Then \(\frac{1}{f(2022)}+\frac{1}{f(2028)}\) is equal to

[JEE Main 2023, 29 Jan (Shift 2)]