Calculus II 
Quiz #10

May 8, 2002

Name____________________ 
R. Hammack

Score ______

(1) Decide if the following series converge or diverge. Explain your
reasoning completely.
(a)
This is an alternating series
with
and .
Therefore, by the Alternating Series Test, it converges.
(b)
Notice that , and
is a divergent pseries.
Therefore, by the comparison test,
diverges.
(c)
Using the Ratio Test, .
It follows that the given series converges.
(d)
This series has positive and negative terms, but it's not alternating. Therefore,
we check for absolute convergence. That involves investigating the series .
Notice that <
and
it follows that
converges by comparison with the convergent geometric series .
Consequently, the original series converges absolutely, so it converges.
(e)
Therefore, by the Divergence Test, the series diverges.