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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.