Question about the Integral Test

[yondy12]

So this is my first post, I was wondering can you explain the first two examples of this page?

http://www.math.ubc.ca/~rathb/mar_6_p_4.jpg

What I don't understand is why, if there is a horizontal asymptote at p = 0.99 < 1 on first example, it diverges to infinity but in the second example, there is also a horizontal asymptote at p = 1.01 > 1 but it converges?

What's the difference and what concept am I not understanding here?

Thanks!

 

[mathman]

The convergence question is only distantly related to the asymptote.
A series with terms 1/n^x diverges for x ≤ 1 and converges for x > 1.

The integral test shows this.

 

[yondy12]

The convergence question is only distantly related to the asymptote.
A series with terms 1/n^x diverges for x ≤ 1 and converges for x > 1.

The integral test shows this.

Ah i realize this is simply a p-series representation. Thanks, that clears it up