Question

Ex 5 punctul b va rog frumos

Answer 1

Explicație pas cu pas:

$a {}^{1} + a {}^{2} + a {}^{3} + ... +a {}^{n} = \frac{a {}^{n + 1}-1 }{a - 1}$

$x = 3{}^{1} + 3 {}^{2} + 3 {}^{3} + ... +3 {}^{2019} = \frac{3 {}^{2019 + 1}-1 }{3 - 1} \\ = \frac{3 {}^{2020}-1 }{2}$

$\sqrt{2x + 1} = \sqrt{2 \times \frac{3 {}^{2020} -1}{2} + 1} = \\ \sqrt{3 {}^{2020}-1 + 1 } =\sqrt{3 {}^{2020}} =3 {}^{1010}$