Question

Oblicz sume ciagu geometrycznego 6 + 3 +... +3/32

Answer 1

a1 = 6

q = 1/2

an = 3/32

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Sn = ?

an = a1*q^(n-1)

czyli

6*(1/2)^(n-1) = 3/32   / : 6

(1/2)^( n -1) = 1/64

czyli

n - 1 = 6  => n = 7

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Mamy obliczyc S7

a1 = 6

a7 = 3/32

n = 7

S7 = a1*[ 1 - q^7]/[ 1 - q ]

S7 = 6*[ 1 - (1/2)^7]/[ 1 - 1/2]

S7 = 6*[ 1 - 1/128]/(1/2)

S7 = 12* ( 127/128) = 3*(127/32) = 381/ 32 = 11  29/32

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