Решение
1) b₁ = 3
Sn = 6
Sn =b₁ / (1 - q)
6*(1 - q) = 3
6 - 6q = 3
6q = 3
q = 1/2
b₂ = b₁ * q
b₂ = 3 * (1/2)
b₂ = 1,5
2) b₇ - b₄ = 168; q = 2
b₇ = b₁ * q⁶
b₄ = b₁*q³
b₁ * q⁶ - b₁*q³ = 168
b₁*(q⁶ - q³) = 168
b₁ =168 / (2⁶ - 2³)
b₁ = 168 / (64 - 8)
b₁ = 168 / 56
b₁ = 3
3) bn = b₁ * q^(n - 1)
q = 16/8 = 2
512 = 8 * [2^(n - 1)]
64 = 2^(n - 1)
2⁶ = 2^(n - 1)
n - 1 = 6
n = 7
4) b₄ - b ₁ = 52
b₁ + b₂ + b₃ = 26
b₁*q³ - b₁ = 52
b₁ + b₁q + b₁q² = 26
b₁(q² - 1) = 52, q³ - 1 ≠ 0, q ≠ 1
b₁( 1 + q + q²) = 26
b₁(q - 1)*(q² + q + 1) = 52
26*(q - 1) = 52
26q = 26 + 52
26q = 78
q = 3
b₁(q³ - 1) = 52
b₁ = 52/(q³ - 1)
b₁ = 52/(26)
b₁ = 2
S₆ = [b₁(1 - q⁶)] / (1 - q)
S₆ = [2*(1 - 3⁶) / (1 - 3)]
S₆ = {2*(1 - 729) / (- 2)]
S₆ = 728
20 мин=120 град
30 мин=180град
0.5 мин=3 град
5 мин= 30 град
4у-5/10 -6у+3/10=
=(4у-5-6у-3)/10=(-2у-8)/10=
=2(-у-4)/10=(-у-4)/5
-4а+3/20 -а-7/20=
=(-4а+3-а+7)/20=(10-5а)/20=
=5(2-а)/20=(2-а)/4
б+3а/а^2 -б-2а/а^2=
=(б+3а-б+2а)/а^2=5а/а^2=5/а
2+х/2х-14 -х-2/2х-14=
=(2+х-х+2)/2(х-7)=4/2(х-7)=
=2/(х-7)
у+2/6-у +у+2/у-6=
=(у+2-у-2)/(6-у)=0
у^2-з/у-з -з^2-з/у-з=
=(у^2-з-з^2+з)/у-з=
(у^2-з^2)/(у-з)=
=(у-з)(у+з)/(у-з)=у+з
Со 2 p-подуровень, с 3 d-подуровень