For what range of values of x will the series 1-2x+4x^2-8x^3+... have a limting sum? What is the value of x if the limting sum is 2/3?
Is it because
Writing this series in sigma notation we have
.
This is a geometric series with and .
The limiting sum of a geometric series is
provided that
In this case, this is
.
But of course, this is provided that
So
.
So the limiting sum is for .
If the limiting sum is then
.