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

Consider a function \(\mathrm{f}:\mathrm{IN}\to \mathrm{IR}\), 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)]