Question

Vă rog mult ajutor,doar la d!​

Answer 1

Explicație pas cu pas:

d)

$x - 4 = 3(4 + {4}^{2} + {4}^{3} + ... + {4}^{n + 2})$

$x - 4 = 3 \cdot \frac{4 \cdot ({4}^{n + 2} - 1)}{4 - 1} \\ x - 4 = 3 \cdot \frac{{4}^{n + 3} - 4}{3} \\ x - 4 = {4}^{n + 3} - 4 \iff x = {4}^{n + 3} \\x = {( {2}^{2} )}^{n + 3} \implies x = {({2}^{n + 3})}^{2}$

$\sqrt{x} = \sqrt{{({2}^{n + 3})}^{2} } \iff \sqrt{x} = {2}^{n + 3}$