1/(xk-xk²) = -1/(xk²-xk) =
= -1/(xk(xk-1)) = -(1/(xk-1) - 1/xk) =
= 1/xk - 1/(xk-1)
=> suma 1/(xk-xk²) = 1/x1+1/x2+...+1/x20 -(1/(x1-1)+1/(x2-1)+...+1/(x20-1) =
= S19 / S20 + suma (1/(1-xk)) =
= 0 + suma (1/(1-xk)).
f'(x) = suma f(x)/(x-xk)
f'(1) = suma f(1)/(1-xk)
f'(1) = 5 suma 1/(1-xk)
(20+10+5) = 5 suma 1/(1-xk)
=> 35 = 5 suma (1/(1-xk)
=> suma (1/(1-xk)) = 7
[tex] \Rightarrow \sum\limits_{k=1}^{20} \dfrac{1}{x_k - x_k^2} = 7[/tex]
