pcvt said:From there I get down to finding for what values the limsup of 1/n x^(2^n/n) is less than one for
I believe its |x|<=1 but I'm not sure how to analytically prove this
A series is an infinite sequence of numbers, where each term is added to the previous term to create a sum. The radius of convergence is a value that determines the interval in which the series will converge, or approach a finite limit.
The radius of convergence for a tricky series is determined by using the ratio test or the root test. These tests analyze the behavior of the terms in the series to determine if it will converge or diverge.
No, the radius of convergence can only be positive or zero. Negative values do not make sense in the context of a series, as it represents the distance from the center of convergence.
If the radius of convergence is infinite, it means that the series will converge for all values of the variable. This is also known as a power series, where the series can be represented by a polynomial function.
The radius of convergence provides a range of values for which the series will converge. If the value of the variable falls within this range, the series will converge. If the value is outside of this range, the series will diverge.