Răspuns:
1007
Explicație pas cu pas:
[tex]a + b = \Big(\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{2015}\Big) + \Big(\frac{1}{2} + \frac{2}{3} + \frac{3}{4} + ... + \frac{2014}{2015}\Big) = \\ [/tex]
[tex]= \Big( \frac{1}{2} + \frac{1}{2}\Big) + \Big( \frac{1}{3} + \frac{2}{3}\Big) + \Big( \frac{1}{4} + \frac{3}{4}\Big) + ... + \Big( \frac{1}{2015} + \frac{2014}{2015}\Big) \\ [/tex]
[tex]= \underbrace{\frac{2}{2} + \frac{3}{3} + \frac{4}{4} + ... + \frac{2015}{2015}}_{2014 \: \: termeni}[/tex]
[tex]= 1 + 1 + 1 + ... + 1 = 2014[/tex]
[tex]\implies m_{a} = \frac{a + b}{2} = \frac{2014}{2} = \bf 1007 \\ [/tex]
(între 2 și 2015 sunt: 2015 - 2 + 1 = 2014 termeni)
