1.Oblicz sumę 10 wyrazów ciągu geometrycznego jeśli a1=2 q=1/2 2. Czy ciąg an=4^n/5 jest geometryczny?
1
a1 =2
q= 1/2
Sn = a1*(1-q^n)/(1-q) ----------------------------^ potęga
n=10
S10 = 2* (1-1/2^10)/1-1/2
S10 = 2* ( 1-1/1024)/ 1/2
S10 = 2* [ 1023/1024 *2/1) = 2 * 2046/1024 = 4092/1024 = 3 1020/1024 = 3 i 510/517
2
an = 4^n/5
n=1
a1 = 4/5
n=2
a2 = 16/5
n=3
a3 = 64/5
a3/a2 = a2/a1
64/5 : 16/5 = 16/5 : 4/5
64/5 * 5/16 = 16/5 *5/4
4=4 = q------------------iloraz ciagu geometryczny
4=4 = q------------------iloraz ciagu geometrycznego
Tak nasz ciąg jest geometryczny
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
1
a1 =2
q= 1/2
Sn = a1*(1-q^n)/(1-q) ----------------------------^ potęga
n=10
S10 = 2* (1-1/2^10)/1-1/2
S10 = 2* ( 1-1/1024)/ 1/2
S10 = 2* [ 1023/1024 *2/1) = 2 * 2046/1024 = 4092/1024 = 3 1020/1024 = 3 i 510/517
2
an = 4^n/5
n=1
a1 = 4/5
n=2
a2 = 16/5
n=3
a3 = 64/5
a3/a2 = a2/a1
64/5 : 16/5 = 16/5 : 4/5
64/5 * 5/16 = 16/5 *5/4
4=4 = q------------------iloraz ciagu geometryczny
1
a1 =2
q= 1/2
Sn = a1*(1-q^n)/(1-q) ----------------------------^ potęga
n=10
S10 = 2* (1-1/2^10)/1-1/2
S10 = 2* ( 1-1/1024)/ 1/2
S10 = 2* [ 1023/1024 *2/1) = 2 * 2046/1024 = 4092/1024 = 3 1020/1024 = 3 i 510/517
2
an = 4^n/5
n=1
a1 = 4/5
n=2
a2 = 16/5
n=3
a3 = 64/5
a3/a2 = a2/a1
64/5 : 16/5 = 16/5 : 4/5
64/5 * 5/16 = 16/5 *5/4
4=4 = q------------------iloraz ciagu geometrycznego
Tak nasz ciąg jest geometryczny