Question

Considere a série numérica abaixo:



Marque a alternativa que determina a soma desta série.

Alternativas:

a) 2

b) 3

c) 4

d) 5

e) 6

Answer 1

Progressão geométrica:

a(n) = a₁ . $q^{n-1}$

a₂ = a₁ . $q^{1}$

3/4 = 3/2 . q

q = 3/4 ÷ 3/2

q = 3/4 . 2/3

q = 6/12

q = 1/2

Elementos:

q = 1/2

a₁ = 3/2

a(n) = 3/1024

a(n) = 3/2 . $(1/2)^{n-1}$

3/1024 = 3/2 . $(1/2)^{x}$

$(1/2)^{x}$ = 3/1024 ÷ 3/2

$(1/2)^{x}$ = 3/1024 . 2/3

$(1/2)^{x}$ = 6/3072

$(1/2)^{x}$ = 1/512

$(1/2)^{x}$ = $(1/2)^{9}$

x = 9

n - 1 = 9

n = 9 + 1

n = 10

S(n) = [a₁ . ($q^{n}$ - 1)]/(q - 1)

S₁₀ = [3/2 . ($(1/2)^{10}$ - 1)]/(1/2 - 1)

S₁₀ = [3/2 . ($\frac{1}{1024}$ - 1)]/-1/2

S₁₀ = ($\frac{3}{2048}$ - $\frac{3}{2}$)/-1/2

S₁₀ = (0,00146484375 - 1,5)/-0,5

S₁₀ = -1,49853515625/-0,5

S₁₀ ≈ 2,99

Resposta: alternativa B