Question

fie numerele a= 1/2+2/3+3/4+...+2012/2013 si b=1/2+1/3+1/4+...+1/2013.Calculati media aritmetica a numereleor a si b.(/=pe)

Answer 1

[tex]a=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{2012}{2013}\\ \\ b=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2013}\\ \\ m_a=\frac{a+b}{2}\\ \\ m_a=\frac{\frac{1}{2}+\frac{2}{3}+..+\frac{2012}{2013}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{2} \\ \\ m_a=\frac{(\frac{1}{2}+\frac{1}{2})+(\frac{1}{3}+\frac{2}{3})+...+(\frac{1}{2013}+\frac{2012}{2013})}{2}\\ m_a=\frac{1+1+1+...+1(de\ 2012\ ori)}{2}\\ m_a=\frac{2012}{2}\Rightarrow \boxed{\boxed{\boxed{m_a=1006}}}[/tex]