Question

Oblicz mając dane Sn=19 i 11/6 (ułamek) q=1/2 i an=5/16 a1 i n.

Answer 1

Oblicz mając dane Sn=19 i 11/6 (ułamek) q=1/2 i an=5/16 a1 i n.
Sn=a1*(1-q^n)/(1-q)
19 i 11/6=a1*(1-(1/2)^n)/(1-1/2)
125/6=a1*(1-(1/2)^n)/(1/2)
125/6=2a1*(1-1/(2)^n)
125/12=a1*(1-1/(2)^n)

an=5/16=a1*q^n-1
5/16=a1*(1/2)^n-1
5/16=a1*(1/2)^n:1/2
5/16=2a1*(1/2)^n
5/32=a1*(1/2)^n
(1/2)^n=5/(32a1)

125/12=a1*(1-(1/2)^n)
125/12=a1*(1-5/(32a1))
125/12=a1-5/32
a1=125/12-5/32
a1=1000/96-40/96
a1=960/96
a1=10

(1/2)^n=5/320
(1/2)^n=1/64
(1/2)^n=(1/2)^6
n=6