Question

calculati mediaaritmetica a numerelor:
a=1pe2+1 pe 3+1pe4+................+1pe 2011
b=1pe2+2pe3+3pe4+..............2010pe2011
Va rog mult ajutati.ma

Answer 1

Dupa cum se observa, cele 2 sume au fiecare cate un numar cu acelasi numitor, formand perechi:

[tex]a+b=( \frac{1}{2} + \frac{1}{2} )+( \frac{1}{3} + \frac{2}{3} )+( \frac{1}{4} + \frac{3}{4} )+...+ (\frac{1}{2011} + \frac{2010}{2011} )\\ a+b= \frac{1+1}{2} + \frac{1+2}{3} + \frac{1+3}{4} +...+ \frac{1+2010}{2011}\\ a+b= \frac{2}{2} + \frac{3}{3} + \frac{4}{4} +... +\frac{2011}{2011}\\ a+b=1*2010=2010 \\ \frac{a+b}{2}= \frac{2010}{2}=1005 [/tex]