Question

Ajutati ma la 8 , la punctul b)

La a) rezultatul este 2 supra x(x+1)

Answer 1

Răspuns:

Explicație pas cu pas:

$E(x)=\frac{2}{x(x+1)} \\E(1)+E(2)+E(3)+...+E(10)=\frac{2}{1*2}+\frac{2}{2*3}+\frac{2}{3*4}+...+\frac{2}{10*11} =2*( \frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+...+\frac{1}{10*11} )=2*(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11})=2*(\frac{1}{1} -\frac{1}{11})=2*\frac{10}{11} =\frac{20}{11}=1\frac{9}{11}$