Question

Find the sum to infinite G.P. 2, ½, ¼, 1/8, ....​

Answer 1

Answer:

S = 8/3

Step-by-step explanation:

Now, in the GP, let a = 2, a₂ = 1/2

Since it is already given that the series is a GP, r = a₂/a

r = (1/2)/2 => r = 1/4

Since |r| < 1, the series is converging to 0

So, In case of an infinite converging series,

S∞ = a/1-r

S = 2/(1-1/4)

S = 2/(3/4)

S = 8/3