Question

47 Calculaţi: a (-2)²+(-2)²+(-2)³ + ... + (-2) 100, = b (-3)¹ +(-3)² + (−3)³ + ... + (-3) 75 =​

Answer 1

Răspuns:

progresie geometrică

Explicație pas cu pas:

$b_{1} = -2; q = -2; n = 100$

$a = {( - 2)}^{1} + {( - 2)}^{2} + {( - 2)}^{3} + ... + {( - 2)}^{100} = \\ = \frac{( - 2) \cdot \Big[{( - 2)}^{100} - 1\Big]}{( - 2) - 1} = \frac{{( - 2)}^{101} + 2}{ - 3} \\ = \frac{ - {2}^{101} + 2}{ - 3} = \bf \frac{{2}^{101} - 2}{3}$

$b_{1} = -3; q = -3; n = 75$

$b = {( - 3)}^{1} + {( - 3)}^{2} + {( - 3)}^{3} + ... + {( - )}^{75} = \\ = \frac{( - 3) \cdot \Big[{( - 3)}^{75} - 1\Big]}{( - 3) - 1} = \frac{{( - 3)}^{76} + 3}{ - 4} \\ = \bf - \frac{{3}^{76} + 3}{4}$