\(M=-\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{n\left(n+4\right)}\right)\\ =-\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n}-\dfrac{1}{n+4}\right)\\ =-\left(1-\dfrac{1}{n+4}\right)\\ =-\left(\dfrac{n+3}{n+4}\right)\)
\(-4x\left(x-5\right)-2x\left(8-2x\right)=-3\\ \Rightarrow-4x^2+20x-16x+4x^2=-3\\ \Rightarrow4x=-3\\ \Rightarrow x=-\dfrac{3}{4}\)
a) \(M=-\dfrac{4}{1.5}-\dfrac{4}{5.9}-...-\dfrac{4}{\left(n-4\right)n}\)
⇔ \(M=-\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{\left(n-4\right)n}\right)\)
⇔ \(M=-\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n-4}-\dfrac{1}{n}\right)\)
⇔ \(M=-\left(1-\dfrac{1}{n}\right)\)
⇔ \(M=-\dfrac{n-1}{n}\)
b) - 4x(x - 5) - 2x(8 - 2x) = -3
⇔ -4x2 + 20x - 16x + 4x2 = -3
⇔ 4x = -3
⇔ x = \(-\dfrac{3}{4}\)
