Odpowiedzi

2009-10-25T18:53:02+01:00
A - pierwszy wyraz
q - iloraz

a + aq = 20
a - 2 = q

a + aq = 20
a + a(a - 2) = 20
2a² - 2a - 20 = 0
a² - a - 10 = 0
Δ = 1 + 40 = 41
√Δ = √41

a₁ = (1 + √41)/2
a₂ = (1 - √41)/2
a > 0

a = a₁ = (1 + √41)/2

a - 2 = q
q = (1 + √41)/2 - 2 = (√41 - 3)/2
S_n = (1 + √41)/2 (1 - ((√41 - 3)/2)^n)/(1 - (√41 - 3)/2) = (1 + √41)/2 (1 - ((√41 - 3)/2)^n)/((4 - √41)/2) = (1 + √41) (1 - ((√41 - 3)/2)^n)/(4 - √41)