$-\frac{1}{4} + (-\frac{1}{4})^2 + (-\frac{1}{4})^3 = -\frac{1}{4} + \frac{1}{16} - \frac{1}{64} = \frac{-16 + 4 - 1}{64} = \frac{-13}{64} = -0,203125$;
$-\frac{1}{3} - (-\frac{1}{3})^2 - (-\frac{1}{3})^3 = -\frac{1}{3} - \frac{1}{9} + \frac{1}{27} = \frac{-9 - 3 + 1}{27} = \frac{-11}{27} = -0,407407...$;
−0,203125 > −0,407407..., значит:
$-\frac{1}{4} + (-\frac{1}{4})^2 + (-\frac{1}{4})^3 > -\frac{1}{3} - (-\frac{1}{3})^2 - (-\frac{1}{3})^3$.

$(-\frac{1}{2})^5 - (-\frac{1}{2})^3 - \frac{1}{2} = -\frac{1}{32} + \frac{1}{8} - \frac{1}{2} = \frac{-1 + 4 - 16}{32} = -\frac{13}{32} = -0,40625$;
$(-\frac{1}{5})^3 - (-\frac{1}{5})^2 - \frac{1}{5} = -\frac{1}{125} - \frac{1}{25} - \frac{1}{5} = \frac{-1 - 5 - 25}{125} = -\frac{31}{125} = -0,248$;
−0,40625 < −0,248, значит:
$(-\frac{1}{2})^5 - (-\frac{1}{2})^3 - \frac{1}{2} < (-\frac{1}{5})^3 - (-\frac{1}{5})^2 - \frac{1}{5}$.