1-Calcular a soma dos termos da PG(1/3;1/6;1/12;...) OBS:É uma PG com número de termos infinito.
2-Calcular o valor x na equação:
x/4+×/8+×/16+...=16
Soluções para a tarefa
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a) PG(1/3;1/6;1/12;...) a1 = 1/3 q= a2/a1= 1/6/1/3 = 1/6 x 3/1 = 3/6 = 1/2
s∞ = a1/1-q
s∞ =1/3 / 1-1/2
s∞ = 1/3 / 1/2
s∞ =1/3 x 2/1
s∞ =2/3
b) x/4+×/8+×/16+...=16
s∞ = a1/1-q s∞ =16 a1 = x/4 q = a2/a1 q= x/8 / x/4 = x/8 . 4/x = 4/8=1/2
16= x/4 /1-1/2
16=x/4 / 1/2
16= x/4 . 2/1
16 = 2x/4
16 . 4 = 2x . 1
64 = 2x
x= 64/2
x= 32
s∞ = a1/1-q
s∞ =1/3 / 1-1/2
s∞ = 1/3 / 1/2
s∞ =1/3 x 2/1
s∞ =2/3
b) x/4+×/8+×/16+...=16
s∞ = a1/1-q s∞ =16 a1 = x/4 q = a2/a1 q= x/8 / x/4 = x/8 . 4/x = 4/8=1/2
16= x/4 /1-1/2
16=x/4 / 1/2
16= x/4 . 2/1
16 = 2x/4
16 . 4 = 2x . 1
64 = 2x
x= 64/2
x= 32
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