[tex]\bf a)\\ \\ \it \dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\ ...\ +\dfrac{1}{30} < \underbrace{\it\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\ ...\ \dfrac{1}{6}}_{25\ termeni\ egali}=25\cdot\dfrac{1}{6}=\dfrac{25}{6} < \dfrac{30}{6}=5[/tex]
[tex]\bf b)\\ \\ \it \dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\ ...\ +\dfrac{1}{30} > \underbrace{\it \dfrac{1}{30}+\dfrac{1}{30}+\dfrac{1}{30}+\ ...\ +\dfrac{1}{30}}_{25\ termeni\ egali}=25\cdot\dfrac{1}{30}=\dfrac{\ 25^{(5}}{30}=\dfrac{5}{6}[/tex]
