Question

Calcule a soma dos 10 primeiros termos da pg (1024,512,256)

Answer 1

a1 = 1024
a2 = 512
q = a2/a1 = 512/1024
q = 2^9 / 2^10
q = 1/2
n = 10
Sn = a1.(1-q^n)/(1-q)
S10 = 1024 . (1-(1/2)10 / (1-1/2)
S10 = 1024 . (1/1/1024) / 1/2
S10 = 2^10 . (1.1024.1) / 1/2
S10 = 2^10 . (1.2^10.1)/1/2
S10 = 2^10 . 2^10 . 2-¹
S10 = 2^19

Answer 2

a1 =  1024
a2 = a1q = 512
q = 512/1024 = 1/2 = 0.5****
n = 10

SOMA SEM FÓRMULA
PG = 1024,512,256,128,64,32,16,8,4,2
1024 + 512+256+128+64+32+16+8+4+2 =2046
pela  fórmula
S10 = 1024 [( 1/2)^10  - 1/1)]/ ( 1/2 -1/1)
S10 = 1024[( 1/1024 - 1/1)] / ( -1/2)
S10 = 1024 [ - 1023/1024] / ( - 1/2 )
S10 = (1024) ( -1023/1024) * ( - 2/1)
S10 =  2046