[tex]\displaystyle{ f(x) = (\frac{1}{2})^{x} }[/tex]
[tex]\displaystyle{ f(0) = (\frac{1}{2})^{0} = 1 }[/tex]
[tex]\displaystyle{ f(1) = (\frac{1}{2})^{1} = \frac{1}{2} }[/tex]
[tex]\displaystyle{ f(2) = (\frac{1}{2})^{2} = \frac{1}{4} }[/tex]
[tex]\displaystyle{ f(3) = (\frac{1}{2})^{3} = \frac{1}{8} }[/tex]
[tex]\displaystyle{ f(4) = (\frac{1}{2})^{4} = \frac{1}{16} }[/tex]
[tex]\displaystyle{ f(0)+f(1)+f(2)+f(3)+f(4) = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} }[/tex]
- se amplifică fiecare fracție astfel încât să obținem numitorul comun 16
[tex]\displaystyle{ S = ^{16)}1 + ^{8)}\frac{1}{2} + ^{4)}\frac{1}{4} + ^{2)}\frac{1}{8} + \frac{1}{16} }[/tex]
[tex]\displaystyle{ S = \frac{16}{16} + \frac{8}{16} + \frac{4}{16} + \frac{2}{16} + \frac{1}{16} }[/tex]
[tex]\displaystyle{ \boxed{S=\frac{31}{16}} }[/tex]
