Question

Calulati media aritmetica a numerelor
a=1/2+1/3+1/4+.....+1/2011 si
b=1/2+2/3+3/4+......+2010/2011

Answer 1

$a \;si\;b \;\; au \;fiecare\;cate\;2010\;termeni \\ \\ M_{a}= \frac{a+b}{2} \\ \\ a+b= \\ =( \frac{1}{2} + \frac{1}{3} + \frac{1}{4}+...+ \frac{1}{2011} )+( \frac{1}{2} + \frac{2}{3} + \frac{3}{4}+...+ \frac{2010}{2011} )= \\ \\ (\frac{1}{2}+\frac{1}{2})+(\frac{1}{3}+\frac{2}{3})+(\frac{1}{4}+\frac{3}{4})+...+( \frac{1}{2011}+ \frac{2010}{2011})= \\ \\ =\frac{2}{2} +\frac{3}{3}+\frac{4}{4}+...+\frac{2011}{2011}=1+1+1+...+1 \;\;\;(\text{de 2010 ori}) \;\;\; = 2010$

$M_{a}= \frac{a+b}{2}= \frac{2010}{2}=\boxed{1005}$