What is the Interval of Convergence for \sum x^n/4^n*ln(n) using the Ratio Test?

[Sabricd]

$$\sum$$ x^n/4^n*ln(n)

I have applied the Ratio Test and I got 1 and I am trying to find the interval of convergence. However, by the Ratio Test, the answer is inconclusive. It does not prove whether it is convergent or divergent. Any ideas?

Thanks!

 

[Mark44]

$$\sum$$ x^n/4^n*ln(n)

I have applied the Ratio Test and I got 1 and I am trying to find the interval of convergence. However, by the Ratio Test, the answer is inconclusive. It does not prove whether it is convergent or divergent. Any ideas?

Thanks!

Just checking... Is this the sum you're working with?
$$\sum \frac{x^n}{4^n}n~ln(n)$$

 

[Sabricd]

Hello,

Nope, it is x^n/(4^n * Ln(n))

Thank you, I think I am just having trouble applying the Ratio Test.

 

[Sabricd]

There is no extra n, and the Ln(n) goes in the denominator :)

 

[IsometricPion]

So the sum is: $$\sum_{n=0}^{\infty}{\frac{x^{n}}{4^{n}\ln(n)}}$$. Could you show how you reached your conclusions? The ratio of consecutive x-coefficients is not one. Even if it were one, that would not mean that the result is inconclusive (it would mean that the sum is a constant multiple of the geometric series which has a radius of convergence of 1).