Consider a function f: N → R, satisfying f(1)+2 f(2)+3 f(3)+…+x f(x)=x(x+1) f(x); x ≥ 2 with f(1)=1. Then 1/(f(2022))+1/(f(2028)) is equal to

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