Explicație pas cu pas:
1. n ∈ N
[tex] \frac{1}{9} < \frac{1}{2n + 1}< 1 \\ 9 > 2n + 1 > 1 \\ 8 > 2n > 0 \\ 4 > n > 0[/tex]
=> n ∈ {1; 2; 3}
2.
[tex][ \frac{3}{4}+ \frac{2}{3} \div ( \frac{3}{4} - \frac{1}{2} )] \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{2}{3} \div \frac{3 - 2}{4}) \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{2}{3} \div \frac{1}{4}) \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{2}{3} \times 4) \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{8}{3}) \times \frac{6}{41} \\ = \frac{3 \times 3 + 8 \times 4}{4 \times 3} \times \frac{6}{41} \\ = \frac{9 + 32}{12} \times \frac{6}{41} \\ = \frac{41}{12} \times \frac{6}{41} = \frac{1}{2} [/tex]
