Question

Cele doua randuri subliniate va rog mult​

Answer 1

Se aduna nr cu același numitor.

Ma = (a+b) / 2 = 1006

Answer 2

$m_a\frac{a+b}{2}=\frac{(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{2012}{2013})+(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013})}{2}=\\ \\=\frac{(\frac{1}{2}+\frac{1}{2})+(\frac{2}{3}+\frac{1}{3})+(\frac{3}{4}+\frac{1}{4})+...+(\frac{2012}{2013}+\frac{1}{2013})}{2}=\\ \\=\frac{\frac{2}{2}+\frac{3}{3}+\frac{4}{4}+...+\frac{2013}{2013}}{2}=\frac{1+1+1+...+1~(de~2013-2+1=2012~ori~1)}{2}=\\ \\=\frac{2012}{2}=\\ \\ =\boxed{1006}$