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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)   1e^(-1),  2e^(-2),  3e^(-3), 4e^(-4),  ...  , n e^(-n),  ...

 




(b)    {n/(5n + 15) + cos(π n)/n^2} _ (n = 1)^∞

 





(c)    {(-n)^3/(6n^3 + n^2 + 3)} _ (n = 1)^∞

 

 


(2)   Consider the sequence  1/2^(1/2),     (1/21/3)^(1/2),    (1/21/31/4)^(1/2),    (1/21/31/41/5)^(1/2), ...
Decide if this sequence converges or diverges. Explain your reasoning.