SOLUTION: The first two terms of an infinite geometric sequence, in order, are 2log2x, log2x, where x > 0. found that r = 1/2. how can I find that the sum of the infinite sequence is 4lo

Algebra ->  Sequences-and-series -> SOLUTION: The first two terms of an infinite geometric sequence, in order, are 2log2x, log2x, where x > 0. found that r = 1/2. how can I find that the sum of the infinite sequence is 4lo      Log On


   

Question 1104418: The first two terms of an infinite geometric sequence, in order, are 2log2x, log2x, where x > 0.
found that r = 1/2.
how can I find that the sum of the infinite sequence is 4log2x?
Found 2 solutions by rothauserc, Boreal:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
r < 1 means that the sum converges
:
Sum = a / (1 - r) = 2log2x / (1 - 1/2) = 4log2x
:
Note that a is the first term
:

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Sum is a(1-r^n)/(1-r), and r is 1/2, where a is 2 log 2x. As n gets large, r^n approaches 0.
sum is 2log 2x(1/(1/2))=4 log 2x