Question

Sa se calculeze suma progresiei 1/3+1/3^2+1/3^3+…1/3^16

Answer 1

Răspuns:

Din păcate eunu știu matematica sunt varza la mate

Answer 2

Explicație pas cu pas:

progresie geometrică

$S_{n} = \dfrac{b_{1}\cdot ({q}^{n} - 1) }{q - 1}$

$b_{1} = \dfrac{1}{3} \ ; \ q = \dfrac{1}{3} \ ; \ n = 16$

$S_{16} = \dfrac{\dfrac{1}{3}\cdot \Big[{\Big(\dfrac{1}{3}\Big)}^{16} - 1\Big]}{\dfrac{1}{3} - 1} = \dfrac{\dfrac{1}{3}\cdot \Big[{\Big(\dfrac{1}{3}\Big)}^{16} - 1\Big]}{ - \dfrac{2}{3}} = \\ = \dfrac{1 - {\Big(\dfrac{1}{3}\Big)}^{16}}{3 \cdot \dfrac{2}{3}} = \dfrac{1 - {\dfrac{1}{ {3}^{16} }}}{2} = \dfrac{{3}^{16} - 1}{2 \cdot {3}^{16}}$