Question

Exercitiul 10 va rog

Answer 1

Explicație pas cu pas:

a)

$\frac{3}{19} < (\frac{1}{5} - \frac{1}{6} + ( \frac{1}{6} - \frac{1}{7} ) + ... + ( \frac{1}{29} - \frac{1}{30} ) < \frac{3}{17} \\ \frac{3}{19} < \frac{1}{5} - \frac{1}{30} < \frac{3}{17} \\ \frac{3}{19} < \frac{1}{6} < \frac{3}{17} \\\frac{3}{19} < \frac{3}{18} < \frac{3}{17}$

b)

$\frac{1}{45} < \frac{1}{21} \leqslant \frac{1}{21} \\\frac{1}{45} < \frac{1}{22} < \frac{1}{21} \\\frac{1}{45} < \frac{1}{23} < \frac{1}{21} \\ ... \\\frac{1}{45} \leqslant \frac{1}{45} < \frac{1}{21} \\ adunam \: termenii\\ \frac{25}{45} < \frac{1}{21} + ... + \frac{1}{45} < \frac{25}{21} \\ \frac{5}{9} < \frac{1}{21} + ... + \frac{1}{45} < \frac{25}{21}$

c)

$\frac{1}{60} < \frac{1}{41} < \frac{1}{40} \\ ... \\ \frac{1}{60} \leqslant \frac{1}{60} < \frac{1}{40} \\adunam \: termenii \\ \frac{20}{60} < \frac{1}{41} + ... + \frac{1}{60} < \frac{20}{40} \\ \frac{22}{60} < \frac{20}{60} < \frac{1}{41} + ... + \frac{1}{60} < 0.5 \\\frac{11}{30} < \frac{1}{41} + ... + \frac{1}{60} < 0.5$