Question

В геометрической прогрессии {an} вычислите S6, если a1=48, q=-1/2

Answer 1

$a_1=48; q=-\frac{1}{2}$
$S_n=a_1*\frac{q^n-1}{q-1}$
$S_6=48*\frac{(\frac{1}{2})^6-1}{\frac{1}{2}-1}=$
$=48*\frac{1-2^6}{2^6}:\frac{1-2}{2}=48*\frac{(1-2^6)*2}{2^6*(1-2)}=$
$=48*\frac{2^6-1}{2^5}=48*\frac{64-1}{32}=94.5$
ответ: 94.5