Question

b1=0,4
$q = \sqrt{2}$
S6-? ​

Answer 1

$b_1=0,4$

$q=\sqrt{2}$

$n=6$

$S_6-?$

Решение

$S_n=\frac{b_1(1-q^n)}{1-q}$

$S_6=\frac{0,4*(1-(\sqrt{2})^6)}{1-\sqrt{2} }$

$S_6=\frac{0,4*(1-2^3)}{1-\sqrt{2} }=\frac{0,4*(-7)}{1-\sqrt{2} }= \frac{-2,8}{1-\sqrt{2} }=\frac{-2,8*(1+\sqrt{2} )}{(1-\sqrt{2} )(1+\sqrt{2} )}=\frac{-2,8*(1+\sqrt{2} )}{1^2-(\sqrt{2})^2}= \frac{-2,8*(1+\sqrt{2} )}{1-2}=$

$=\frac{-2,8*(1+\sqrt{2} )}{-1}=2,8*(1+\sqrt{2} )=2,8+2,8\sqrt{2}$

$S_6=2,8+2,8\sqrt{2}$