You are welcome.

]]>So my new answer is:

Therefore, series converges for k>=2]]>

That is what I mean, something is bad where I indicated. There could be further mistakes but that is where the first one occurs.

]]>I do not think there are mistakes:

Or are you talking about different equations?

The second line is not correc(k(n+1))!=1*2*3*...*(k(n+1)-1)*(k(n+1))

]]>Shouldn't manipulations maintain equality with the original assertion?

That does not?

]]>Or are you talking about different equations?]]>

Something is wrong right there.

]]>For which positive integers

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...

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