<span>Первый член прогрессии: A1 = -0.25
Найдем n-ый член прогрессии: An = A1·q<span> n - 1</span>
A7 = (-0.25)·(2)7-1 = -16
Сумма первых n членов прогрессии: Sn = A1·(qn- 1)/(q - 1)
S7 = -0.25·(27- 1)/(2 - 1) = -31.75
<span>Первые 10 членов прогрессии: </span>
A1 = -0.25
A2 = A1·q = -0.5
A3 = A1·q2 = -1
A4 = A1·q3 = -2
A5 = A1·q4 = -4
A6 = A1·q5 = -8
A7 = A1·q6 = -16
</span>
<span>((</span><span>1+cosx)/2+(1+cos3x)/2)-1=0;</span>
<span>1+cosx+1+cos3x-2=0;</span>
<span>cos3x+cosx=0;</span>
<span>2cos(3x+x)/2*cos(3x-x)/2=0;</span>
<span>2cos*2xcosx=0;</span>
<span>cos2x=0 (1); cosx=0 (2)
</span>
<span>(1) 2x= </span><span>π/2+π</span><span>n;</span><span> x=π/4+πn/2
(2) x=π/2+πn
</span>
Ответ: x= π/4+πn/2; x=π/2+πn
Sina sinb + cos(a+b) = sina sinb + cosa cosb - sina sinb = cosa cosb = 1/2 (cos (a+b) + cos (a-b))