Question

calculați media aritmetică a numerelor:

a= 1/2 + 1/3 + 1/4 + .... + 1/2011 și b= 1/2 + 2/3 + 3/4 + ..... + 2010/2011

Answer 1

[tex]a=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+_{\dots}+\frac{1}{2011}\\ \\ b=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+_{\dots}+\frac{2010}{2011}\\ \\ m_a=\frac{a+b}{2}\\ m_a=\dfrac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+_{\dots}+\frac{1}{2011}+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+_{\dots}+\frac{2010}{2011}}{2}\\ m_a=\dfrac{\left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{1}{3}+\frac{2}{3}\right)+_{\dots}+\left(\frac{1}{2011}+\frac{2010}{2011}\right)}{2}\\ ~~~~~~~~~~~De\ 2010\ ori\\ m_a=\frac{\overbrace{1+1+_{\dots}+ 1}}{2}[/tex]
$m_a=\frac{2010}{2}=\boxed{1005}$