Question

find the sum of the infinite geometric series, if possible.
8+6+9/2+27/8........
and the book says the answer it 32. Explain, anybody?? I don't understand what pattern or rule this set of numbers is following....

Answer 1

it looks like: each term is being multiplied by 3/4.

Answer 2

\[\sum_{n=0}^{\infty}8(3/4)^{n}\] so it's a geometric series

Answer 3

|r| < 1 so it converges to 8/(1-3/4) = 8/(1/4) = 32