Question

What is the sum of this infinite geometric series?

∞
∑(12)(0.5)^i
i=1

Answer 1

well list a few terms

i = 1 6

i = 2 3

i = 3 1.5

i = 4 0.75

to the common ratio r = 1/2

the 1st term is 6

so the infinite sum can be found by

\[S_{\infty} = \frac{a}{(1 - r)}\]