Question

1) Determine a soma dos termos das seguintes PG’s infinitas: a) (1/2; 1/4, ...) b) (2; 1/3;...) c) (10; 2/5; ...) d) (2; -¾; ...) e) (10; 5; 5/2; ...)

Answer 1

Resposta:

Explicação passo-a-passo:

Soma da PG infinita:

Sn = a1/ (1-q)

a) (1/2; 1/4, ...)

q = a2/a1 = 1/4 / 1/2 = 1/4 * 2 = 2/4 = 1/2

Sn = 1/2 / (1-1/2)

Sn = 1/2 / 1/2

Sn = 1/2 * 2

Sn = 1

b) (2; 1/3;...)

q = 1/3 / 2 = 1/3 * 1/2 = 1/6

Sn = 2 / (1-1/6)

Sn = 2 / 5/6

Sn = 2 * 6/5

Sn = 12/5 ou 2,4

c) (10; 2/5; ...)

q = 2/5 / 10 = 2/5 * 1/10 = 2/50 = 1/25

Sn = 10 / (1-1/25)

Sn = 10 / 24/25

Sn = 10 * 25/24

Sn = 250/24

Sn = 125/12

d) (2; -¾; ...)

q = (-3/4)/2 = -3/4 * 1/2 = -3/8

Sn = 2 / (1--3/8)

Sn = 2 / (1+3/8)

Sn = 2 / (11/8)

Sn = 2 * 8/11

Sn = 16/11

e) (10; 5; 5/2; ...)

q = 5/10 = 1/2

Sn = 10 / (1-1/2)

Sn = 10 / 1/2

Sn = 10 * 2

Sn = 20