Question

exercitiul 41 va rog frumos!!​

Answer 1

$A = 3 {}^{n + 1} \cdot 2 {}^{n} + 3 {}^{n + 2} \cdot 2 {}^{n + 1} - 16 \cdot 6 {}^{n} \\ A = 3 {}^{n} \cdot3 \cdot 2 {}^{n} + 3 {}^{n} \cdot3 {}^{2} \cdot 2 {}^{n} \cdot 2 {}^{} - 16 \cdot 6 {}^{n} \\ A = (3 \cdot2) {}^{n} \cdot3 + 3 {}^{n} \cdot9\cdot2 {}^{n} \cdot2 - 16\cdot6 {}^{n} \\ A = 6 {}^{n} \cdot3 + (3\cdot2) {}^{n} \cdot18 - 16\cdot6 {}^{n} \\ A = 6 {}^{n} \cdot3 + 6 {}^{n} \cdot18 - 16\cdot6 {}^{n} \\ A = 6 {}^{n} \cdot(3 + 18 - 16) \\ \boxed{A = 6 {}^{n} \cdot\red5}$