The problem is:

For which positive integers *k* is the following series convergent?

My Answer:

For series to be convergent the next inequality should be true (by the Ratio Test):

Since we know that both k and n are positive we can omit absolute bars.

And now I simplify:

But since

*k* is a constant this limit will never be less than 1. Therefore the series divergent for all possible

*k*.

Did I make a mistake somewhere? Textbook is looking for a convergent series...