Explicație pas cu pas:
[tex]{2}^{n + 3} + {2}^{n + 2} + {2}^{n + 1} \\ ={2}^{n + 1} \times {2}^{2} + {2}^{n + 1} \times {2}^{1} + {2}^{n + 1} \\ = {2}^{n + 1} \times (4 + 2 + 1) \\ = 7 \times {2}^{n + 1}[/tex]
[tex]{3}^{2n + 3} + {3}^{2n + 2} +2 \times {3}^{2n + 1} = {3}^{2n + 1} \times {3}^{2} + {3}^{2n + 1} \times {3}^{1} +2 \times {3}^{2n + 1} ={3}^{2n + 1} \times ( {3}^{2} + {3}^{1} + 2) = {3}^{2n + 1} \times (9 + 3 + 2) = 14 \times {3}^{2n + 1}[/tex]
[tex]3 \times {2}^{3n + 1} - 5 \times {2}^{3n} + 7 \times {2}^{3n + 2} = 3 \times2 \times {2}^{3n} - 5 \times {2}^{3n} + 7 \times {2}^{2} \times {2}^{3n} = {2}^{3n} \times (6 - 5 + 28) = 29 \times {2}^{3n}[/tex]
