Calculus II 
Quiz #8

April 24, 2002

Name____________________ 
R. Hammack

Score ______

(1) Decide if the following sequences converge or diverge. In the case
of convergence, state the limit.
(a) ln(1), ln(1/2), ln(1/3), ln(1/4), ... ,
ln(1/n), ...
This sequence diverges because ln(1/n) = ln(n) approaches
negative infinity as n approaches infinity.
(b)
= 2+0 = 2
Thus the sequence converges to 2.
(c)
cos(1/n)
= cos 0 = 1
(form ∞ 0) (form
0/0)
The sequence converges to 1.
(2) Consider the sequence
...
Decide if this sequence converges or diverges. Explain your reasoning.
Notice that every term of this sequence is positive, and it decreases because
any one term is obtained from the previous term by multiplying by a positive
number that
is less than 1. Therefore this sequence is a decreasing sequence that is bounded
below by 0. Therefore, by Theorem 11.2.4, it converges.