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Calculus  II                                                             Quiz #8                                             April 28, 2003

Name____________________                        R.  Hammock                                         Score ______
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(1) Decide if the following sequences converge or diverge. In the case of convergence, state the limit.

(a)   1,  2,  3, 4,  ...  , ,  ...

The nth term is .  As n goes to infinity, this is an indeterminate form .
Using L'Hospital's rule:
Thus the sequence converges to 0.

(b)

Thus the sequence converges to 1/5.

(c)

Thus the sequence converges to -1/6

(2)
Consider the sequence
Decide if this sequence converges or diverges. Explain your reasoning.

Notice this is a decreasing sequence because

Moreover, the sequence is bounded below by 0.

As a decreasing sequence that is bounded below, it must converge.