Examples 4.2.12:
	Does the series converge or diverge ? Does the series converge or diverge ? Does the series converge or diverge ? (This is the same series as in the example for the Limit Comparison test . Are we running in a circle here ?)

If p < 0 then the sequence converges to infinity. Hence, the series diverges by the Divergence Test.

If p > 0 then consider the series

=

• if 0 < p 1 then 2 ^1-p 1, hence the right-hand series diverges
• if 1 < p then 2 ^1-p < 1, hence the right-hand series converges

Now the result follows from the Cauchy Condensation test .