Question

Find the sum of the series. 1/2^n. n=1 (summation symbol) to infinity.

Answer 1

i know its a geometric series but am not sure how they found a= 1/2 and r= 1/2. I know the formula for a geometric series is a/(1-r)....and that r has to be less than 1.

Answer 2

1/2 + 1/2^2 + 1/2^3 + ... + 1/2^n

1/2 (1 + 1/2 + 1/2^2 + ... + 1/2^n-1)

\[1/2\frac{1-1/2^n}{1-1/2}\]
since |r|<1 r^inf = 0
\[1/2\frac{1}{1-1/2}\]

Answer 3

oh ok, thanks!