Converging Series for ln(n) with Comparison Tests

[goaliematt76]

Homework Statement

Find all positive values of b for which the series Ʃ b^ln(n) converges. Bounds are from n=1 to infinity.

Homework Equations

The assignment is for Direct Comparison Test and Limit Comparison Test.

The Attempt at a Solution

I don't know where to begin. Using a comparison test would only indicate convergence or divergence. It seems like it might be a geometric series, but I'm not sure.

 

[Dick]

Homework Statement

Find all positive values of b for which the series Ʃ b^ln(n) converges. Bounds are from n=1 to infinity.

Homework Equations

The assignment is for Direct Comparison Test and Limit Comparison Test.

The Attempt at a Solution

I don't know where to begin. Using a comparison test would only indicate convergence or divergence. It seems like it might be a geometric series, but I'm not sure.

Try and turn it into a series that looks more familiar. Write b=e^ln(b).