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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.