Functions

Consider a function \(f:\mathbb{N}\to\mathbb{R}\), satisfying \(f(1)+2f(2)+3f(3)+....+xf(x)=x(x+1)f(x);x\ge2\) with \(f(1)=1\). Then \(\frac{1}{f(2022)}+\frac{1}{f(2028)}\) is equal to